If they have a secretary, you could always drop by today and see if you can just pick up the letter. Otherwise, give them another call.
Go to the courthouse on Monday with or without a letter. In some jurisdictions failure to report results in an automatic warrant for arrest. Explain the situation and I am sure you will be immediately released without service. They will generally accept a faxed document. The time to request exemption was when you received the letter. You aren't going to go to jail, but it is best to stay out of the computers.
I agree completely with caregiver. In my area, if you "blow off" jury duty, they send you a warning letter that you must reply within 10 days, or a warrant could be issued. I'm sure it's probably similar in most jurisidictions, however, I wouldn't take a chance.
Your best bet is to show up and the courthouse and explain the situation. I'm sure they will release you, and if they want some kind of documentation from your psych, they will probably give you a certain time frame to produce it. They may not even require paperwork.
You should have handled this right away, to avoid all of this last minuite confusion, both for yourself, or the court system.