I've had chronic tennis elbow (tendonitis) for nearly 40 years. When I do something to cause it to flare up beyond the ordinary background pain, I do two things to effectively reduce the inflammation. First is four (4) 2000 mg ibuprofen tablets twice a day. This is twice the dose recommended in the US, but pretty ordinary in Mexico and S. America. The second is ice, as in ice bath. Dump a full tray of ice cubes in a large bowl and add enough water to cover well. Dunk that elbow for a full ten (10) minutes. No cheating! Set a timer. It will hurt so much at first that you will have to pull your elbow out for a few seconds, but keep at it until you can hold it in the ice water bath.
Doctors and PT told me to ice it by rubbing an ice cube frozen in a styrofoam cup. BS! It was a trainer at the health club I used to attend who told me how to make ice more effective, and she was right. A few days of ice and ibuprofen has always gotten my tendonitis pain back to the background level that I can tolerate forever.
Another thing, stiff fast action graphite fly rods are not friendly to shoulders and elbows that are predisposed to this kind of inflammation. Use medium action, or maybe even a medium fast action rod. Stiff action rods in 9 wt and up will likely always cause this kind of problem for you. I put my 9 wt in the closet years ago and made an 8 wt medium action rod my every day use until I started using Spey rods for all my steelhead fishing. I use a fast action 8 wt for salt water sight fishing, where I'm not making one cast after another from can't see in the morning 'til can't see at night. For all day streamer fishing I use a medium action 6 or 8 wt, and I can hold the tendonitis at bay.