Check on the regulations of your intended destinations - I'm aware of strict UAE rules (on what are mostly prescription drugs in the US, not unregulated supplements), and while they are not often enforced, an American with a one-day layover in DXB got caught and arrested this past January, with a prohibited drug for which he had a prescription.

Nutritional supplements are probably a different story, especially if in original commercial packaging, but what's prescription in one country is non-prescription in another and v.v.

The UAE regs are on the website of their Ministry of Health IIRC; state.gov may have links to other countries' information on its info for travelers pages.