Could this be the start of arthritis?

When I was 10 I broke my L wrist in a bicycle accident. The doctor didn't set the wrist right; the cast was taken off early and I received no physical therapy. My wrist was weakened as a result. 20+ years later I injured the same wrist again in a factory accident. This time the L hand needed surgery. As a result when the weather changes; the hand and wrist are overworked or if I lift a too heavy object I am in pain. I try to keep the hand and wrist limber; exercise as much as possible and I try not to use any pain medication unless necessary. Since arthritis is hereditary in my family could I develop arthritis as well and if so what else can I do? Any advice helpful. Thank you. :)