Hey there. I've been a Byetta user for a few months now. I love it, congrats on starting a wonderful new med.
about traveling . . . it you call the byetta hotline, they will send you a free travel kit complete with ice pak to keep it cool enough to stay good. Other than that, you can have it at room temperature for 144 hours, but it cannot be above room temp.
I'm not sure how big my needles are, but the shot doesn't hurt. I don't even feel it. I inject, push the button down for 5 secs, remove and then hold the injection site on the skin for a few secs so it doesn't leak out.
Byetta is taken before breakfest and before dinner. There is 5 mcg dose and 10 mcg. You start on 5 mcg to get adjusted.
I inject in my thigh. I used to rotate a lot and found that other injection sites made me sick. The thigh has a slower absorption rate than, say, the butt of abdomen. You can see what works best for you.
Hope I could answer some of your questions.