You were injected in the buttock and have pain in shoulder and chest.
It is almost impossible for an intramuscular injection
in buttock to cause pain in shoulder and chest. Also if the nurse had injected it lower down, there was more chance of nerve damage
. Even this nerve is related to legs and not hands and arms.
So, the pain in shoulder is unlikely to be due to injection.
With buttock injection, commonest nerve to be damaged is the sciatic nerve
and usually there is immediate intense pain and weakness of leg after injection.
If you are still worried about the nerve, do a nerve conduction velocity test. And you will need steroids
to help control the damage and heal the nerve.
I feel that this is not due to the injection and advise you to see a physician maybe someone specializing in internal medicine for your symptoms.
Hope this helped. Good luck and take care.