I inject manually, though I have tried the auto-injector thingy too (the noise makes me jump and pull it out too quick DOH!).
When I started on copaxone (3 years ago) I really struggled with it, I'd been on Rebif before and never had a problem. I found that it really hurt after the injection, so much so I would be in tears. The Copaxone nurse came to see me and was a great help...... she was happy with the way I was doing the injections but thought I was a bit allergic to it, hence the pain and the big red lumps and bruises. She advised me to take a 1-a-day antihistamine for a while and to use the gel packs, warm or cold before and after injecting. I found that a warm pack before and a cold pack after, really helped. Once my body got used to it (about 6 weeks) I stopped the antihistamines.
I also got Emla cream (and the plasters to put over it) from my GP, it's the stuff they use in hospitals to numb the area. I got this because I'd developed a bit of a phobia and REALLY struggled to push the needle in. It's a bit of a pain because you have to put it on an hour before you inject, but it really helped me get over that fear. In the end I became allergic to the plasters and had to stop using it but by then I was over the fear and managed fine without it.
I've never had the heart beating fast reaction, I'm sure I will one day but I'll deal with that if/when it happens.
I was told not to inject my arms because there wasn't enough fat there, but alternate all of the other sites each time. I asked the Copaxone nurse to drawer x on my skin on the sites I should use and took photos to refer to, this really helped at the start. Once I got used to it I didn't need to refer to it any more.
I've got big dents on my legs and smaller ones on my tum, my neuro told me to miss those sites out for a while but that didn't help so he told me to change to injecting every other day, which is what I now do. The dents are still there (always will be I think), but they're not getting any worse. They started to appear after being on it for about a year.
The biggest bit of advice I can give you is to make sure you keep your skin in good condition. Use Bio Oil or a soothing body lotion the day after you inject and massage the area well. If your skin it well moisturised, the needle will go in easier, however you inject.
My neuro told me that my experience was definately NOT 'the norm' and most people don't have site reactions as bad as mine. I'm glad I stuck with it though as it's working well for me, with only 1 or 2 small relapses a year (I was having bad relapses every 6 weeks when Rebif stopped working).
Sorry if I've gone on a bit! Good luck.