It's natural to be worried, but the nurse should really help alleviate your worries and answer your questions.
Like others have said (only slightly different) my nurse recommended heat for approx 5 min before (heat pack or rice pack) then the shot- I use the auto injector and somewhere between a 6 and a 7 setting works well for me but it's what is best for you- then pressure with a cotton ball or folded up paper towel (cotton ball works best... something about the shape/pressure it provides) for 30 sec to a minute, then cold compress for 1ish minutes. Stomach and hips are the least painful to me, while thighs and arms are more difficult.
I have to sing "pop goes the weasel" to myself and push the button of the auto injector when I get to the POP part to get myself over freezing up/not wanting to inject myself. Silly, but it works for me.
Hang in there! If you're doing everything "right", the injection itself shouldn't hurt. If the injection does hurt, play with the depth settings... it's either too deep and hit muscle or too shallow and close to the nerves by the skin. There is burning afterwards and that's no fun but with the ice it's bearable and should go away except for some soreness for the next little while (especially if you've been sitting on leg day and then get up to move and it's like "oh yeah! forgot it was leg day... grr...") but reaction/soreness should go away in 24-48 hours at the most.
It's much easier than any other shot I've done (pain shots, progesterone, B12 etc).
Like others have said- you'll do great!
First, don't sweat it piece of cake. Place the shot under your arm to get it body temperature. Rotate shots. Get a warm compress and put it on the injection site. Use the auto injector if you can. Don't go too deep with the shot. If you do the muscle will be a little sore but don't worry about it, it goes away. You will be fine. I never had any side effects at all when I was on it.
I took Copaxone for over 4 years and of course it is only natural to be terrified but believe me it isn't as bad as it would seem. The burning after hurts more than the injection. Good luck...you will do great!!
Take a Tylenol about a hour before
When I started, I called a nurse for about a week or two until get used with the idea. Dont be shame of have fear of it, with time you'll get used and soon will be like tooth brush :-)
I really recommend to put ice before and after the injection and take note of the spots that you use to make sure that you will not repeat. I avoid take hot bath before and after the injection and I wait a few minutes just to the body "take" the copaxone peacefully. ;-) Good luck!