Your tendons have tightened and shortened with the repetition of wfp work. The only real cure is stretching them out again and this will take time. An injection will only mask the pain. In fact injections for tendonitis are no longer recommended in all but the most serious cases and seen as a last resort. If not administered properly an injection can cause permanent damage to the tendon. No, I'm not an expert but this is how it was explained to me by a specialist earlier this year. Having suffered it before 10 years ago and knowing how painful the effects of the injection can be for a few days after ( sometimes even worse than the original discomfort ) I was happy to take their advice. I've followed their instruction on stretching plus have tried to add an even and broader range of movement and grip in both arms and hands whilst working. And although not completely free from tennis elbow yet, 8 months on its remarkably better and although I can still feel it, does not hinder or prevent me from working.
There is a Velcro fastening strap you can buy that adds support and compresses the inflamed area of the tendon and gives some pain relief whilst working.
Massage the area as much as you can too, there are YouTube videos on the most effective way to do this, it will promote blood flow which in turn will aid the healing process.