What did the doctor say? Did he tell you to rest it for those 2 months? Hmm, he gave you a wrist brace to give your arm more strength, but not an elbow brace too?
While I am not a doctor or physio specialist, my thought is that you should rest it a bit for a short while to see if it starts to heal. The doctor said 2 months (which is about 8 weeks). Whenever I have injured a muscle or joint, I rest it a while to let it heal, then resume my hand-weights and toning exercises, etc; but I start out gently, doing less, then building up over time.
When I hurt one of my shoulders, a physio person had me do some light exercises at first, but that just hurt it even more. I stopped for a while, and when the pain had left completely, I started to do more a bit at a time. That worked better for me; and my regular doctor agreed with my plan becuz he said the pain was a signal that I had an injury that needed to heal first -- meaning it needed to rest.
Hope this helps a bit ... JMHO.