Can you locate exactly where you had your jab?
If you get your jab into the outside extremities of your deltoid muscle it could possibly hit the axillary or radial nerve and this can cause some temporary issues which will be slow to subside.
Additionally if your vaccination goes in too high it can end up in your shoulder bursa and that can cause inflammation in the joint which can also last for weeks. The other potential complications can be if the injection was delivered too deep and hits the bone.
If it persists it is worth getting it checked out but afaik the only solution once any of the above happens is to just give it time to sort itself out.
I am not a trained medical practitioner or Dr Jazz though, I've just done the vaccination training and been told where not to stick the needle
Hope it heals for you soon. Just had a full rebuild of my shoulder and it's pain you can definitely live without.
Frieda