As a professor - I get students who have all sorts of things come up. I don't actually think that much about it. I direct the students to the dean of students for my part of the university and let them handle it if the student appears to be struggling across the board. If the student needs to withdraw/get some sort of medical leave or accommodation etc - it is not a big deal to me. I prefer not having to read a lot of reasons/excuses/things that are really not my business - I like the designated administrator to handle it -unless it is unique to just my one class.
I really suggest you contact the dean of students (or who ever is designated to take care of student issues at your university/college) and let them help you negotiate with the faculty since it sounds like this may be a bigger issue than just one paper or something like that.