Hkaya

Hey! I am in the exact same situation as yours, waiting since June 30. My classes are also beginning next week. Believe me, I tried to do my best to get my visa in time. I tried every possible way to find out how my visa can get stamped before the classes begin. I contacted the Embassy in Turkey several times via e-mail and by calling. I also attempted to contact the White House by sending e-mails to Mr. President twice and the First Lady once, as well as sending e-mails to the Department of Justice. I reached out to people who happened to have connections inside the Embassy, but it wasn't helpful either. Even my supervisor sent a petition to the Department of State in the U.S. Each passing day made me realize more how my hands were tied in such a unique situation.
Believe it or not, I also went through the psychological breakdown that you are having (I still kind of am). But, the least I can tell you is that no university or professor is going to take away your right to education because of a bureaucratic obstacle that you have absolutely no influence or control over. All you have to do is to send your professors an explanatory e-mail, express your sorrow and your determination for your research field. You will see how understanding and helpful they will be. Most likely, your TA or RA offer or whatever you're given will be secured one way or another.
In the meantime, you can take this opportunity to spend some time for yourself. Plan a trip to South America or something like that. I know that's what I will be doing!
Cheer up!