Well, I got my next injection, this time in my right leg and no problems with swelling and redness. The muscle is a bit sore, sure, but no problems. The nurse said most likely what happened is I didn't stab the needle in fast enough the last time. I also grabbed a big chunk of leg and squeezed upward because I heard that helps as well.
So, now I think I know where I went wrong. Good also to know that I don't have to switch the injection site to my rear!