Some recent thoughts re; good/bad here -
https://canadianbrawn.com/threads/training-after-cortisone-shot-in-hand.4138/ . I'm on the pro side for sure mostly due to personal and anecdotal reports and lack of science either way as discussed in that thread. I've had a few in each elbow for Tennis elbow and a bunch in my shoulders and biceps. Most of them were pretty painless or mild at best. The bad one feel like you got hit with a 100 mile an hour slap shot for a day or two.
I said that I was on the pro side but I hope you give rehab a serious shot first. 3 months isn't long compared to some. I've had a lot of success using eccentric only rehab exercises for tendon issues including the therabar. A bunch of times it has worked for me in less than a week. About half the people I've used it with get relief really quick and the other half get pretty much nothing from it, at least short term. Great videos out there of reverse wrist curls and therabar stuff.
I've only used the cortisone when I get stuck in a loop of partial recovery and then worsening symptoms that I can't break out of. Used the cortisone to allow me to put some serious rehab time in without inflammation getting in the way.