You should talk to your doctor and not necessarily rely solely on advice for medical needs from the internet.
That said, most docs will give you a couple Ambien to try. You say you're sensitive to medicines but that is really dependent on your own body and differs from person to person.
Ambien also has a pretty short half-life so it's generally processed and out of your system within a few hours.
It CAN, however, have some interesting side effects (It's a hypnotic) so it's definitely best to try at home first.
For me, for example, I can pop an ambien once I'm on the plane, and I'm good until the first beverage service and dinner, then I'm asleep for a few hours, then I wake again. Ambien has less of an affect on me than it does my friend, who was woozy for several hours after taking one.
Another example, using me, I can't take anything with diphenhydramine in it (benadryl, used in most otc sleep aids) because even the pediatric dose of 12.5mg will knock me out for at least a solid 18 hours and hung over for most of the next day. I'm super sensitive to benadryl.
But when I go to the dentist, I have to have double the normal dose of anasthetic because I process it so quickly that the normal dose wears out before the dentist is done.
So point is, you should talk to your doctor and just tell them "Hey, weve got a long trip coming up, I'd like to try an Ambien to see if that will help me sleep and not leave me feeling hungover".
Other things to try:
Lunesta (but it's longer lasting)
Restoril (also longer acting)
OTC:
Sometimes 30mg of melatonin usually will help me as well.
I've tried Valerian, but hate the aftertaste it leaves.
Also, I sleep with a set of Bose QC-20is in so the noise is kept to a minimum, YMMV. Point is, go ask your doctor about good ideas for sleep aids. My GP is pretty good about recommending both prescription and OTC remedies where appropriate.