Very sorry to hear you are having difficulty.
I just started Copaxone in late February this year. I've gotten used to giving my injections for the most part. Had difficulty for the first month, simply because of the psychological aspect that comes along with shooting yourself up. But, now its more or less routine. The needle itself for the most part, doesn't hurt and sometimes only feels like a puff of air against my skin. I use the Autoject 2 and its an absolute godsend for administering the shot. I don't think I could do it manually. If your shots are REALLY hurting, you may be injecting to deep, hitting the muscle instead of staying subcutaneous.
I am male, 5'9", 152lbs..so there ain't too much subq fat on my bod. On my hips and belly I use a 6mm setting which seems to be perfect, no shot pain, just the 2-3 minute burn of the mannitol which you aren't going to be able to avoid. Mannitol, which suspends the galtirmer acetate is an alcohol and sugar based solution.....it burns, get used to it. I was using the same 6mm setting on my arms and thighs early on and it was leaving them sore for the whole week, feeling better only just in time to get popped again on the next rotation to that site. I talked to one of the Shared Solutions nurses and she highly recommended I dial back the Autoject setting to 4mm and that has helped tremendously with the site soreness on my thighs and arms. Now, its 2 minutes of burn, followed by maybe 2 - 4 hours of site swelling (what i call the "Copaxone Areola"), and then maybe another half day of mild tenderness. By the time the site rolls around to the next rotation, its good to go.
Injections hurt. There's really no way around it. My good friend, who has type I diabetes and has to shoot insulin all the time, sometimes up to 8 times a day when she's not able to wear or use her insulin pump basically told me, "Quit being such a pussy! This is your life. You do what you gotta do." Truer words were never spoken.
Now, I tend to view any pain I feel from the injections as sort of a rite of passage. I adapt and overcome. I was in the Army for 6 years and when ever things seemed bad, we had a mantra that was always said with a smile and a laugh.....
"Man, I LOVE how much this sucks!!"
Wishing you all the best