NO IMMOBILIZATION! NO ICE!!! These are the basics.

Meds, including Lidoderm patches or cream are good to research. Warm water PT or baths with Epsom salts. A Stellate Ganglion Block via fluoroscopy by an experienced doc would be worth considering. Ketamine. HBOT. Etc...

And your doc has likely not seen much RSD if he's expecting spread to occur that way. It CAN, but it is not at all uncommon for it to happen in the manner you described.