At least under the Peter Singer style formulation of human respect for animal welfare, not eating meat is predicated on our actual capability of doing so without endangering or greatly burdening ourselves (same as with our obligation to be charitable outlined in Famine, Affluence, and Morality). This is why “would you eat meat on a desert island”-style questions can be easily answered “yes” without undermining our own values. For the tremendous majority of people, they indeed would not be endangered or greatly burdened by not eating meat. However, you find yourself in a place where that is no longer true. I think we have all met someone for whom their veganism is a cover for an eating disorder. I am not going to allege that is true of you, but I will gently suggest that you follow your psych’s guidance as they are a professional who is best acquainted with your situation and who wants to help you. When you find yourself on stable ground again, you can return to not eating meat. The important thing here is that you eat now without guilt.

Well, you’re basically in the same situation as kids who have non-vegan parents forcing them to eat meat.

I don’t know in what jurisdiction you are, but in some places, they definitely have to accommodate for religious reasons, for example. You could attempt to inform them; in some cases, it might help change their minds.

But yeah, if they truly want to force you to do something and have a large number of people surrounding you, there isn’t much you can do on a practical basis, regardless of whether you are in the right or not.