Be very very careful when feeling any pain in your arms, wrist, shoulders, and dont just ignore them, as pain is a warning that something is not happy. It is usually easy to tell the difference between good pain (as in a stifness froma good workout, and bad pain - shooting / stabbing pains arent good)
I leant this the hard way through ignoring a pain in my shoulder joint, until after one class i could no longer lift my arm above shoulder height. We thought i had Rotar Cuff and Bicep Tendonitis - but after Physio, scans and and x-ray discovered i actually had Sub-Deltoid Bursitis (inflamation of the Bursa in my shoulder joint) Bursa are fluid filled sac in most joints, and are there to help the tendons, muscles etc glide over each other when in motion. Through overuse it becomes inflames and swells, in an already small space this causes to much friction and begins to catch on things instead of allowing for smooth movement - bloody sore i tell you! Thankfully through rest and going to a Biokineticist to learn how to engage ALL the muscles correctly i am slowly getting better and can now brush my hair again and clean my teeth. BUT NO POLING FOR A WHILE STILL...Arrgh.
As a result i know get a sharp pain in my elbow when i use that arm, due to other muscles overcompensating, and cheating to allow me to do things. This sounds like what you are experiencing - possibly using the wrong muscles to support your weight in pole sits etc, and causing stress. The body is a funny thing in how it works out ways INCORRECTLY to allow us to perform moves - and we dont even realise we are using the wrong muscles. So yes work on strengthening forearms, wrists front and back shoulder muscles - and if possible find a pole teacher who can show you what muscles you should be engaging when -hard as im not sure many even know themselves - i asked my Instructor if she was taught such things and she had no idea :(
Arm and shoulder injuries are very common in pole, so dont ignore an ongoing pain, otherwise you may put yourself out of action for a while - like silly me did!
Apologies for the essay...lol. Good luck