If you’ve always felt push ups more in the deltoids than the chest, it sounds like you may not know how to put the tension on your chest, yet I suspect it is due to an underlying issue with some kind of structural alignment rather than simply poor technique.
Honestly, I would suggest working on bridges and Australian pull ups extensively. Try to work push ups as well, but if they keep giving you issues I’d suggest trying bridge push ups, or possibly dips, if they don’t bother your shoulders. For the bridge push ups, ultimately you want to touch the back of your shoulders to the ground at the bottom of every rep. But you don’t really “have” to do push ups, for the time being you could just work on holding bridges for time.
I’d also recommend hanging leg raises, I think they could be good for your shoulders, plus they’re great for your abs.
Besides all that, you may want to find a good chiropractor or physical therapist. Most regular doctors will probably just give you pills and maybe recommend surgery.