Hello Karen,
You've come the right place, although I'm so sorry for the reason.
What a freak accident!

I've had rsd for over 27 years. It sounds as if you may have some TOS (thoracic outlet syndrome) involvement there too. As do I. (There is another thread on NT here, for that).
I'm glad you got such a quick diagnoses, (took me 7 years). They've got to be aggressive enough with your pain relief, so that you can do some stretching, but, I'd be careful about any kind of strengthening exercise. See if they don't torque up your headaches!

Your body will tell you what works/doesn't.
As you say the ice or heat. If they don't work, chuck 'em. (I use ice packs on my head, for headaches, but not for rsd, and most people will say they don't like ice on the rsd). Moist heat may come to work for neck, shoulder area.
Get some Eucerin (they make one called 'calming itch relief' too) or something like that for your right hand. (It dries from the inappropriate perspiration, the rsd).

I'd suggest that you talk to your neuro about more pain control (if you need it for therapy), and ask about TOS. He may want to send you to a hand specialist.

You'll have lots of friends here. If you like, you can PM me.

Also, I suggest you get over to to
www.rsdsa.org
Join.
It's a source of wonderful information.
Keep in mind too, that this disorder is 'Managed', not too often cured. But, you got a dx early, and that's your best chance to put it in remission. Do your reading and gather knowledge, all you can!

I wish you all the best, keep your chin up and appreciate all the good things!

Pete

ASB