This story remind me a lot of my grad school experience, which was only a few years ago. I wasn't diagnosed with narcolepsy (that was this year), but I was diagnosed with clinical depression / OCD, and it was tough. Are you, by chance, in the sciences? I don't know if it's like this in other fields, but I did feel like there was some element of "if you can't keep up, you shouldn't be a scientist," which is absurd. Science is not a field that requires superhuman stamina (being a tenured professor at the kind of large research school I went to may well have been--but there are lots of places for scientists to work!).
A couple of things:
1) I started narcolepsy about four or five months ago. It's also been very effective for me! Anxiety is a common side effect. I knew that, I knew it would be unpleasant, but my doctor thought there was a really good chance it would lessen over time. Since I already had anxiety issues (OCD is an anxiety disorder), I knew it might get ugly. And, I have to tell you, the first month was not fun. But it gradually got better, and I feel like I did before--my anxiety/OCD is well-managed. Also, if after a few months on the nuvigil, the anxiety does not go away, there may be something they can do medically to help with that. Ask your neurologist, or perhaps he/she will refer you to a psychiatrist. I've never had panic attacks, but I understand they can be successfully treated! I also took yoga and meditation classes at my university when I was diagnosed with OCD, and that helped a lot. It was nice to have had all that "how to cope with anxiety" experience under my belt when the nuvigil side effects came on, because even though I would frequently have the urge to punch my coworkers in the face

, I knew how to talk myself down and calm myself.
2) Find the office at your university that assists students with disabilities. Narcolepsy qualifies as a medical condition under the Americans with Disabilities Act. Not to say that you or I or anyone else is "disabled" by it, but employers are required by law to provide "reasonable accommodation." In my case, this has meant working scheduled naps into my workday (purpley is so right! if I don't schedule them, they don't happen... and these little power naps are so helpful!). Make an appointment to go talk with a counselor or someone in that office. They can explain what your rights are, and what your professor's responsibility, etc. Not that you want to go stomping into his office reading him the riot act, but if you know what your legal rights are, that can be helpful.
3) It's absolutely not too much to ask to take an unpaid leave while getting medical issues under control. Under FMLA (family and medical leave act... I think) you're entitled to take a medical leave of absence without losing your job. It's even partially paid. If you're being paid as part of a graduate assistantship, I'm not sure how that works, and if FMLA applies... but perhaps there's something in your university policies about medical leaves. The office for students with disabilities can probably help with that info, too.
4) It's weird to me that your professor is so understanding of personal situations on the one hand, and yet rather un-understanding on this one. It makes me wonder if maybe he just really doesn't know too much about narcolepsy, or has never had experience with someone managing a chronic illness and yet finding professional success. You might need to be the one to educate him about this. Hopefully your doctor or a school counselor can help you navigate this. I had a really fantastic graduate research advisor--he really did care, and was so super helpful. He was German, and he was rather the stereotypical German scientist--a little reserved and standoffish. A very kind man, really, but not all warm and fuzzy. When I told him about the depression/OCD that I was navigating, he was concerned, but he had no idea how to help me. He would ask things like, "Do you want to skip this research trip if you're not feeling well?" And no, I absolutely did not want to skip the research trip, I just sometimes needed extra time to run my data--and sometimes I didn't. He may really be willing to accommodate what you need once he understands a) what it is and

that eventually you're going to get into a routine that really works for you, and then your productivity won't be as sporadic.
And you absolutely will. Hang in there! Find out what resources you have at your university and let them help you learn how to advocate for yourself! And keep us posted!