I just got one of these and used it on a recent trip to store some meds, Tylenol, etc. It worked very well and felt very secure, even the inside doors have some resistance, so I don't feel that any of them would open up accidentally.
It is a bit thick but if you're packing many types of medications it would be bulky nonetheless. I carried it every day in my sling and it worked great.
Each day (with two compartments per day) on this pops out, so you could just take 1 or 2 with you.
This could also be an option - you can have 1, 2, or 3 sections.
I also have one that I can't find the link for that might be overkill. It's similar to the second one above in size and shape (maybe a bit larger), but opens in half with separately sealed sections on each half. One was divided, the other wasn't - I used to store q tips in the undivided side. I'm sure someone still makes them. If that sounds like something you might want, I can try to find something similar.
Edit: like this but one side was all one section.
Not sure if the way it closes is secure or not, unless you put a band around it