For a different opinion -- I always put my OTC vitamins and supplements in individual clear ziplock baggies. I label each baggie (with a white address label) with the name, strength, lot #, expiry date and NPN (natural product number). I'm Canadian and I've done this on dozens of trips to the US and Europe. It's never been an issue for me. I keep them all together in my checked luggage.
For actual OTC medications (Tylenol, Benadryl etc) I do keep those in their original bottles and will usually buy a smaller size just for travel.
Vitamins and supplements are not technically "drugs" which is why they have a NPN and not a DIN (drug identification number). Maybe I've just been lucky but I've never had trouble. If you're going to do it I would recommend identifying the vitamins/supplements in some manner -- I'm not sure that I'd use a pill case.
Just my two cents.
This is what I do, as the bottles my vitamins/supplements come in are too large for travel (even the smallest size that can be bought) and some of them are glass which is just downright unsafe for travel.
Vitamins/supplements in individual clear Ziploc (I find the snack size work well), with a printed address label with the supplement's info. No mixing of supplements -- so the Citracal go in their bag, the vitamin C goes in its bag. Since I have quite a few, I have also gone onto the manufacturer's websites and copied the label information and made 4x6 cards that I print onto photo paper -- 1 for each supplement. Those cards are carried in the same container as the Ziplocs with the supplements. I have never been asked, but the info is there if needed.
Actual OTC meds I also buy a smaller sized container just for travel so they are in their original container [if pills in a blister pack, I will take the sheet out and cut the front of the box of and slide it in the ziploc holding the sheet].
Rx meds I will get the pharmacy to give me an extra labeled smallest-possible bottle for each med for travel -- they do this free. I now have one of each for each Rx med (that is in pill form) and I just refill it from the larger bottles when I travel.
I then bring an EMPTY pill sorter (Dosett, but there are many brands) and when I get to my destination I fill it; for longer trips I refill it partway through the trip.
Note: I make sure all supplements, OTC meds, and Rx meds I travel with are legal to bring into the country I am visiting [and then back home]. Different countries have different rules, and it can apply to supplements or OTC or Rx meds. e.g. what is OTC in one country may require an Rx in another country. A supplement you can buy off the shelf in one country may be outright illegal in another. And some countries have very specific rules about some Rx meds or meds in certian forms (e.g. injectibles/syringes) where they may not be allowed to be imported at all, or there you may have to get advance permission. Sometimes a country will let a resident of another country bring in a medication for personal use but subject it to quantity limits; this is especially the case if a med is OTC in one country but Rx in the destination. Never assume just because a supplement or medication (vitamin/supplement, OTC or Rx) is fine in your home country that it is the same elsewhere.
SW