I talked to another of my professors today, which leaves one more to talk to-- this professor has agreed to give me an incomplete and time this summer to finish my work in that class. Instead of homework to turn in, he offered me three exams which will determine my grade. He did ask for additional documentation from my doctor, so I'll call the VA in the morning and talk to either my doc or someone else on my assigned team. Then that'll be done. I've never had any problems asking for and receiving letters for school from any of my VA providers. (As one of them explained, any provider you see in the mental health clinic has been in college. They understand why you need the letter.)
About incompletes in general: at my school, an I means you have until the next regular semester starts to complete your work for a course. It's up to you to ask each professor, and to provide additional documentation if they ask. Your school may be different, so check your undergraduate catalog (you know, that book you got at orientation and haven't read yet).
If you're in my situation, and finals are next week, and you have no idea how you're going to pass this semester-- talk to your professors, your adviser, your dean, somebody. Those people usually know what PTSD and mental health issues mean, and they'll probably be willing to work with you.