I have a Jacuzzi bathtub and soak often. I don't have a regular outside hot tub, but it's the same principal. In the winter there is just nothing better for me than a hot bath. I have cold CRPS and in the winter I can literally feel me thawing out as I submerge myself. Of course I'm like a wet noodle and bed is the ONLY thing that will happen afterwards. My muscles seem to appreciate it and it tends to relax everything.
I have made the mistake of taking a hot bath and then try to go somewhere where walking was required. Big mistake!

Huge! Other than that, yes, this therapy works well for me.
Goosebumps: yes... random and sometimes often. I have read that this is part of the gig. It has something to do with our cooling mechanism being broken.
Shocks and vibrations: I too have both of these symptoms. The electric shock is definitely a CRPS symptom and the vibrations, for me these too are part of the gig. I have developed tremors over the years and sometimes my body will just hum (vibrate) before an actual tremor starts. I don't know if you're old enough to remember that in hotels WAY back in the day, you'd put a quarter in to make the bed vibrate. My husband jokes with me that we don't need quarters for our bed... just me... lol
So sorry that you're dealing with this too! No fun at all.