My mom is a nurse, and therefore, was always prepared for every bump, scrape and sting my brother and I got when we took family vacations. Following in her footsteps, I always take a fully stocked first aid kit with me when traveling internationally.
I pack everything in one of these plastic packing envelopes, with a few of the more frequently used items – like hand sanitizer – in my carry on. I try to keep everything its original packaging if it’s not too bulky (although I don’t bring boxes), but if I have a few loose pills, I put them in a small baggie and affix the label from the bottle.
I recommend bringing Western products with you, since you might not be able to find them easily on the road, and if you do, the quality might not be what you are used to. You can always incorporate any local, natural cures you find along the way – when I came down with a terrible rash in Cambodia, lemons were the only thing that relieved the itching! Also, keep in mind that in many countries, you can easily get antibiotics and other medication without a prescription – when I was living in Nepal, I had frequent bouts of strep throat, but I was able to walk to a pharmacy and get a cycle of amoxicillin for about 50 cents.