The travel pack that Lilly sends you only keeps it cool for an hour or two. Its pretty useless. Medicool has a pack especially for byetta. http://www.medicool.com/diabetes/diabetes_travel_protectallbc.html . Supposed to keep it cool for 8 hours. Another suggestion I read online is put a few ice cubes in a baggie and put that in a stanley thermos. Been told it works for much longer than 8 hours.
Some hints to help the nausea. OTC antacids and acid inhibitors. Pepto Bismol helped me the most. Accupressure wrist bands (found them at my local pharmacy) helped tremendously. Finally, prescription drugs if none of the above work. All these things need to be done one hour prior to the shot as a preventative to work best. I've been on it for a couple months, now, and am finally starting to feel better again. What really helped was a three day sebaticle from the drug. After a brief time off, when I went back on, everything was fine.