This isn't a perfect tool, but for a first pass at drug interactions, check out this link:
https://go.drugbank.com/drug-interaction-checker
I don't know your particular circumstance, but I think the most likely circumstance -- a shot to relieve inflammation or pain, administered infrequently -- would be fine. Cortisone shots aren't given often anyway, since they fuck up the cartilage in joints.
Honestly, HGH and test are probably a great tool for anyone undergoing serious glucocorticoid therapy. It tends to stunt growth in kids, and causes muscle wasting. Those are way better than the alternatives for people in a clinical situation where you *need* heavy glucocorticoids, but still not great.
TLDR: if you need a cortisone shot, get it.