I don't know about spasms specifically, but I lost motion in both of my hands due to arthritis. I had so much inflammation that my wrists couldn't bend them. I also had DeQuarvains, if I'm spelling it right, which is inflammation of the sheething around my thumb tendon. It was incredibly painful! I also had a couple ganglion cysts that struggled to go away.
So what worked for me was seeing an occupational therapist 3x a week for a couple months. Between braces, steroids, massage, therapy, and stretching exercises at home I was able to get my hands back. Occupational therapists are specifically trained to work on hands and arms.
I still had inflammation trouble though, and so I decided to do whatever I could to fight it so I didn't get the problem again. I cut out all gluten and dairy. It helped a lot back then! I now know a lot better that starch and sugar are actually what cause my inflammation, and after totally eliminating both from my diet I hardly have any inflammation issues anymore.
I know my situation isn't the same, but it may be similar enough to help you find answers.