Not sure if your question is still relevant, but just noticed it and thought I'd reply.
I've been getting allergy injections for about 40 years.
I've been giving myself Copaxone injections for almost 2 years.
So far, they've gone fine together. I should note that I don't use my arms for Copaxone injections; I save them for the allergy shots. Part of my motivation is that my arms are relatively lean, and my shot nurse warned that this might make the arm shots more painful, since Copaxone wants to be injected into the fatty layer below your skin. I did try my arm once for Copaxone, and sure enough, it was a pretty painful shot that ached for a day or two. Instead of my arms, I use my "love handles", e.g. the sides of my torso. Those aren't Teva-approved sites, but my shot nurse and neurologist both said they're fine.