After a few months the side effects (wasp sting feeling) went away and I only have one now if I jab in the wrong place.
A quick way to help, if you don't want to bother with coldpacks, is a wet cold cloth, or hold a glass of cold water against the site for a minute.
If you want to get really scared, google Copaxone side effects. The list is long and very varied. Most people don't get them, but be prepared. I got swollen lymph nodes. My gyno panicked, he thought it was cancer, and sent me to hospital on the same day where they took some out to look at. They were perfectly innocent, my poor little lymph nodes. Now they swell up from time to time, but always go down again. I also have dark patches on my lower arms in summer, quite harmless, don't bother anyone but me. So if you get some strange symptom, check the list first and show it to your doctor if you think it could be relevant.
Bibo ergo sum