You need to talk with your doctor about your medicines. Most doctors will write you a prescription to accomodate your cruising routine. I'd also carry a certified copy of my medical record
if you need to consult a doctor anywhere you are or the authorities question your stock of drugs.
When we were out many years ago, our doctor gave us samples that the drug companies plied him with. Didn't cost us anything other than the medical visit and stocked our medicine chest with a lot of prescription drugs. He also gave us an expired copy of the PDR which was immensely helpful evaluating the drugs we had when we had to treat an affliction based on the symptoms.
If you need drugs that are subject to deterioration and/or require refrigeration
(insulin), you are going to have to get refills along the way. In third world countries, drugs aren't as closely guarded by the pharmacists. You can get a lot of drugs without a prescription. In any case, a prescription will get you what you need. Having your medical records would facilitate getting a local prescription if that became necessary.
Last but not least, don't get hooked on prescription drugs. Quite often folk remedies will work just as well. I used up most of our supply of anti-biotics treating a recurring staph infection. Cured it in a couple of days with a weak bleech solution. BTW, the bleach solution was advocated by a cruising MD.