Hello Faith!
Copaxone is my first MS drug. I'm almost to the 3 month complete mark. No looking back. I've never used the Autoinjector (it's there to use if you choose, whether you do the shots with this or manually, entirely up to you!). I don't pre-heat or pre-ice either, or do either after the shot.
I found the worst for me was the 20ish min. site burn after the injection. At the point I am now, I still get this in some locations. The first area for the burning to cease was the 2 spots on the lower back (just above the bum) in my case. Also, I don't find the thighs burn much (the injection part on the thighs, plus the after bump, was what I experienced, more in a bit!). The tummy for me still has the most burn after shot to this day, followed by my arms.
After I do my shot, I take my cotton ball and press down firmly on the injection spot for about 30 seconds after. I find this DRASTICALLY reduced any amount of lump after the injection (thanks Dej for this one!!!). This was the best "tip" I learned

.
Other than that, for the thighs, I find holding 2 inches of skin between 2 fingers for about 2 min before my shot really helps numb the area for injection 'pain'. Overall though, the needle is so tiny, that most of the time the injection of the needle itself doesn't hurt me. Sometimes I come across an area with tougher skin and have to use more force (that's no fun!) but overall, as a newbie myself, I find Copax is very tolerable, convenient and easy to get used to.