Or, you could just pack your diapers in a separate bag. Then when checking in for your flight, declare you have a bag for medical reasons. Most every carrier will allow one free bag to be checked if it is for medical purposes. Of course, you will need to be ready to tell them what is inside. Also, with some airlines you will need to fill out a small card to present to them for your medical declaration. Usually it's just something you can download off their website and print out before hand.
Alternatively, when you get to the USA, look for actual medical supply stores. They often carry half-decent diapers, which will likely be enough to get you through your trip. Forget about looking for diapers in any local pharmacy or food & drugs store. What they carry won't hold crap- quite literally.