You might try taking an antihistamine like benadryl a couple of hours before injecting. Benadryl also provides anti-emetic effects as well. Note that the non-drowsy antihistamines don’t have the additional anti-emetic effect.
Site irritation such as you describe suggests an allergic reaction. This may not really go away, I would talk to your doctor about this. You may just react to some of the ingredients and may do better on a different formulation of a GLP-1.