Hi and welcome.
I'm guessing you're talking about Copaxone. I was on it for a couple of months and had to stop, so I don't know long term about the stinging. When I injected it, I too would get quite a bad sting, which lasted up to an hour. It did begin to get shorter, though, so I just waited it out.
I'm not a medical professional, but I see no reason why not to take ibuprofen, acetaminophen or similar in advance of injection, if it helps you.