I'm sorry your T wasn't very helpful. Can you tell him what you said here? I bet the urge to "fix" is really hard to resist sometimes, but I know how invalidating that can be. But I think it might be easier for him to help you if you can tell him what you need from him.
I think it's a similar sort of thing with your professors in terms of asking for what you need. I imagine it will vary from class to class. For the class with the assignment, I might say that I am having mental health problems that are currently being treated, that I have the assignment, and asking if I can turn it in late. Is it something you can send as an attachment? Or drop it off somewhere? Late assignments are really common, and it's likely that your instructor has a policy for dealing with it that would give you a better outcome than not handing it in at all. For the other professors, it might depend on what the consequences are. If they have strict attendance policies, you might just have to take the hit and assume your performance elsewhere will compensate for it. If there are specific things you need help with, it doesn't hurt to ask if they have suggestions. Usually office hours were drop-in (at least when I went to them and when I had them as an instructor), so you wouldn't need an appointment. When I was teaching courses, I always appreciated when students were matter-of-fact about things going on in their lives and dealt with them the way you might do it in a workplace (i.e., not too much detail about specifics, not asking me to take care of them, but being specific about how I could help them be successful in my class).
I don't know if your reasons for being stressed when it sounds like you're actually getting okay grades are like mine. I actually didn't understand my reasons until recently, and I've been out of undergrad for over a decade now. But I do hope you can figure out how to cut yourself a little slack. Even if you get a B (or all B's!), the world won't end and you will still be a worthwhile human being. Please keep coming back and posting as much as you need to.