I began Copaxone back in February and I was really nervous about it as I hate injections! However, three months on and it's just become part of my daily routine. I barely even think about it!
Everyone's experience of the injections seems to be different as we no doubt all have different reactions to things. I read a few horror stories on here, but my own experience turned out to be much less traumatic.
Firstly, my autoinject pen is always set on 8, but I guess this depends how much 'padding' you have! (I have sufficient!) The nurse assured me that, even set on 10, the needle is not long enough to 'damage' anything beyond the skin/fat layer. Like you, my legs have less fat than stomach/hips, and on occasion I have had some bruising, but this goes in a few days.
Post-injection reactions: Initially, in my thighs, I got a flat, raised area and some redness, but this disappeared by the end of the day. Other areas get some redness, but I can often not tell where I've injected a few hours later. Some 'nettle sting', occasional 'bee sting' pain (though not for long), and I have had some itching.
The 'big reaction' that we are warned about (chest tightness, breathlessness) has not occurred thankfully, though I was told that it could happen at any time. I was advised to rest until it passed and to ring the MS nurse. Could you also make sure someone else is around whilst you are doing the injection, in case of a reaction? (I am single and live alone, so I don't have that luxury!)
Now that I have got into the swing of injections, the threat of this 'big reaction' doesn't even cross my mind. I know it's easier said than done, but try not to think about it. After all, if you are relaxed doing the injection you may be less likely to have the reaction (that's the way I look at it!)
I hope you get on OK with the injections. It becomes second nature after a while, and not everyone has the terrible reactions, so try not to dwell on it.