What is the best way to treat tendonitis?

I have tendonitis in my elbow. The pain extends to my upper arm. I do circuit training 3 times per week. I saw a doctor who advised me to stop all upper body equipment until the tendonitis was gone then add one machine back each week. The problem is my tendonitis has never completely healed. It hurts whether or not I have exercised. I take Advil but it gives me very little relief.

If I do my upper body exercises when the pain isn’t especially severe am I doing further damage to my arm?