The fundamental question, here, is why is your department so antagonistic towards you? This is important, not just because it's the "bigger problem" as Dan Romik noted in his answer, but also because the answer changes the answer to your question.
Here are a few possible "bigger problem" explanations, and the resulting answer to your question for each case:
1. You have upset someone in the department with a lot of sway with the rest of the department, who has since spread rumours, etc, about you.
In this case, your first course of action is to reach out to the appropriate anti-bullying body within your institution. Such behaviour is unacceptable, no matter how egregious your action may have been against that person, and the behaviour of the other members of the department are similarly unacceptable. If what you did to upset the person was a real problem, then they should have similarly reported you to that body, not initiated a campaign to destroy you. And if the cause of the upset was completely innocent and minor, then all the more reason to report the situation to the appropriate body.
Once the bullying is addressed, either people begin treating you with basic respect again or you seek to move to a new institution, where the well hasn't been figuratively poisoned. Continuing at an institution in which nobody respects you is not a viable approach, no matter how self-reliant and insular you may want to be.
2. Your own behaviour is causing general upset within the department.
Contrary to the first possibility, this one is indicative of a problem with how you are engaging with the department. In effect, where in case 1 the well is being poisoned by a professor or other person with sway, in this case you are poisoning it yourself (likely without even realising it). If this is the case, there is no realistic method to "get" people to examine your work, etc, without first addressing what it is that you are doing to repel them.
In this case, complaining to an anti-bullying body, or changing institutions, is unlikely to change your experience, at least in the longer term - the same issues that have arisen at your present department will simply reoccur, and this will cause further issues. Even paying people to review your work is likely to only work in the short term, as you will get a reputation quite quickly.
Instead, you need to undertake some self-reflection, to identify what it is that people are responding so badly to. Perhaps you are unconsciously injecting arrogant language into your interactions, or being too flippant to other people when they speak about anything other than your work. Or perhaps you are handling criticism poorly, coming across as defensive and aggressive when people point out flaws. There are many other possible issues, and it is unlikely that anyone here can diagnose the issue - that said, if there is someone who is a little less antagonistic towards you within the department, you could approach them and ask for their perspective.
3. You have misinterpreted signals from those around you.
Sometimes what people say can be misinterpreted. For example, the first professor you mention may have been expressing concern about something, and honestly recommending that you seek mental health support - this is a taboo topic in many places, but there is no shame in seeking such support. And if you are already feeling a lot of anxiety and discomfort about interactions, it can come across as an accusation, rather than an attempt at support.
Similarly, the second professor might have been expressing that you had some weaknesses in your current understanding, and that you were not yet ready for the more complex arguments that are often found in particularly long proofs, etc. This may have been meant as a simple critique, but for a person with anxiety, for example, it can come across as an attack. And the third professor, as noted by astronat in the comments to your question, may have simply been trying to manage expectations - few people get fields medals, and that doesn't mean their contributions aren't worthy.
In this case, I would strongly recommend seeking the mental health support noted earlier. Again, there's nothing to be ashamed of, and seeing a psychiatrist or psychologist doesn't mean you are crazy or unbalanced. Mental health professionals are much like physical health professionals - they treat a wide variety of issues, many of which are quite common and can become debilitating if not kept in check.
In the meantime, self-reflection is again on the cards. Why are people refusing to help you, if there isn't an antagonism issue within the department? The answer to that question will tell you what to do.
4. Their criticisms are sincere and honest.
This is the hardest one for you to contemplate, but it is worth bringing up as a possibility. You may be showing substantial misunderstandings of basic concepts. Note that this doesn't excuse them calling you out publicly, or telling you that it's intrinsic to you (rather than simply being the current state of affairs), but it is still worth considering for yourself.
This could overlap with case 2, in that the Dunning-Kruger effect could be impacting your response to their criticisms. If you do have a fundamental misunderstanding of something key to your field, then it can be hard for you to see it, and hard to accept when someone tells you that you are wrong, because you lack the expertise necessary to understand their criticisms.
This often leads to crank-like behaviour, which can put off those around you as they view you as nothing but a crank. It is not uncommon for people in academia to become extremely wary of cranks, and disengage as quickly as possible. Unfortunately, this then drives those who are simply a little misguided towards crankism.
This, also, will require some self-reflection, but in a different way. Look back at some of the criticism you have received in the past - which portions of the criticism did you accept, and which portions did you reject? Is it possible that the portions you rejected were actually of value? You likely know more now than you did at the time - you may notice that you had rejected criticisms that you now can tell are legitimate.
In this case, your best way forward is to approach someone who may still be a little amenable, and apologise for previous behaviour - then, instead of asking them to review your work, ask for their help with filling gaps in your understanding, using the work to help guide that process.
5. Discrimination is at play.
It saddens me that I need to include this one, but even in academia in 2021, discrimination can be an issue. Are you black in an otherwise-white department? Or white in an otherwise-black department? Are you female, and the professors, etc, are not? Do you identify as trans? Are you vocally atheist or religious? Many of these things can influence how you are treated, sadly.
But keep in mind, this is a two-way possibility. You might be the one discriminating, and they're simply responding. You need to consider this possibility alongside the reverse.
If you are in a department with a discrimination problem, you could try approaching the appropriate discrimination body within the institution, or seek a role in a different institution that you have checked for better diversity. If you are the one discriminating, of course, you should (and I know this keeps coming up) undertake some self-reflection. Either way, the discrimination needs to be addressed before you will be able to get others around you to take your work seriously.
This is not an exhaustive list, but I believe it captures the most likely cases. You will notice that self-reflection is a common thread for most of the cases - this is because of the maxim that "if everyone around you is the problem, maybe you're the problem". I do not provide this as a criticism, but simply a reason why self-reflection may be needed - the only way to tell whether or not you are the source of your own woes is to undertake some self-reflection. And the result of that self-reflection tells you what you need to do.
In any case, as Dan Romik said in his answer, ignoring the bigger issue won't get you anywhere. It might give you a momentary short-term result, but you'll end up right back where you started in short order.
