Hi JAM's Mom,
I'd also suggest seeing a Neurologist but after reading your post I'd also suggest a developmental pediatrician. The part you've written listing the tics sounds like tics. Yes. The rest doesn't.
You've also mentioned he has anxiety or obsessive fears, mood swings and some of the other things you've listed are probably the ones that need sorting out the most. A few of the things that you listed in the Talents section sound a lot like my son when he was the same age and he has a condition called Asperger's Syndrome as well as the TS/tics.
As Chemar said, it's quite common for children not to have tics in the doctor's office but a good doctor who is knowledgeable about TS will understand that. If I was in your shoes it's the anxiety and the mood swings that would be of more concern to me.
I must say that your son sounds wonderfully talented! Just amazing.
Depending on what area you're in will in a way influence who you see about these other issues that your son is dealing with. Here's a website that deals with childhood fears and anxiety. As it explains in there, it's not so much the "things" that a child worries about that is the problem, it's more how much all that worry and anxiety is affecting the child.
http://www.worrywisekids.org/
Tamar Chansky also has some very good books available. One of them is "Freeing your child from anxiety".
So really, it's the anxiety and the mood swings that would be my first priority and in some areas in the world (I'm in Australia) it'd be a Psychiatrist who might be the best type of person to see for those issues. It really depends so much on where you live and who you have available in your area that might be able to help sort out all the issues.
You also might find that the tics settle down a bit once those other issues are smoothed out. The difficult thing is figuring out what's driving the anxiety and the mood swings and that could be quite a number of things, so finding someone who is knowledgeable is the best way to go and the sooner the better for your son. I'd also be thinking about some social skills training if there's anything like that available in your area. That might help your son with his relationship skills especially at school.
TSA-USA has a referral form on their website ...
http://www.tsa-usa.org/forms/prl_aprl_inq_form1005.html
Physicians and Allied Professionals
Referral Lists Inquiry
It might help if you were able to give a general idea of where you're situated as there may be someone else here who has good experience with someone in your area. I don't mean exact details or anything. Just general area. If you do end up finding someone and they dismiss the anxiety and the other details as being part of Tourette's Syndrome and they focus on your son's tics then I personally would suggest that you get another opinion... that's just "my" opinion though.
all the best to you and your son. Let us know how things are going there.
EDITED to add:
site crashed for a few minutes so I couldn't finish posting these...
I don't want to confuse the issue for you JAM's Mom or to worry you more, but did want to post this site in case any of it rang some bells. Sorting it all out can be tedious and it can take a little time, but it'll all be worth it in the long run for your son.
http://www.thegraycenter.org/identifyingachild.cfm
Identifying the child with ASD
By Laurel A. Hoekman