I don't take Byetta, was thinking about it, but when I did a search on it and it took me to a site where 100s of people posted about the side effects from Byetta I decided not to take it. But, a WHOLE LOT of people have the same side effects as you are having so you are not alone.
The losing weight sounded enticing to me but I couldn't even handle 1 week of sickness when I was pregnant with my son so I didn't think I could handle months and months of it. Hope it works for you though.