I had a similar pain to your description when climbing. Held on to a hold too long, little click and I had pain throughout my forearm into my elbow.
Little bit of a strain on the tendon. Advice from my mate who works in muscle rehabilitation post op was keep it heated often, move it in the pain free manner I can often. Keep circulation high as this aids recovery and then continue exercising in means that will be pain free. Also worked on mobility of surrounding joints - wrist and shoulder.
All good now. Followed this and was climbing again 6 weeks later.