I was helped enormously by physical (working on muscles, etc) and occupational (finding workarounds for problem activities) therapies. There are lots of exercises to improve flexibility and strength. There are lots of gadgets and techniques to make difficult activities easier.
My treatment was highly effective and exceeded my expectations given the amount of damage to my hand from an accident.
The treatment used neither medication nor massage.
I have a number of exercises I do daily while driving or watching tv that help a lot, both in terms of relieving pain and increasing strength and flexibility.
Discuss with your doctor and ask him if he would refer you for physical therapy.
I agree with your reluctance to have surgery. Any surgery will leave scar tissue, which makes the problem worse, so try other things first!