It sounds like you "missed" some, possibly all, of the shot. The dead feeling could be nerve damage. I'm not a doctor nor can I tell very much from the picture you sent me so take my advice with a grain of salt.
You asked me if it is something to worry about? I know that if I were in your shoes, I'd be worried. Not to alarm you, but it's the truth. I used IV for quite some time and never had a reaction like you have described.
A warm compress might help. If it gets worse, go to the ER. If your boss has a problem with that, tell her it will take you twice as long to wash the dishes with only one arm.