I'm another one who can say that those itching and burning sensations and the huge lumps from Copaxone shots really do go away as time goes by.
I've been on Copaxone for nearly 3 years now, and I hardly ever have any reactions at all to the shots any more. In fact, I often can't find where the needle went in by the time I'm reaching for the cotton ball to put over the injection site. If I feel around I can sometimes find a tiny bump.
Every once in a while a shot will hurt but nothing like the first few months. And I do still have lumps with the arm shots.
Good luck on Copaxone!