For each country you will be entering, check online (Google for starters seems to work) find the Agency/Authority for "importing drugs". It may be a variation of those words, etc.
That should tell you what is or is not allowed, plus any special permissions, and where to get those. With email these days, we've found that very easy and fast.
It can be oddball. Japan will not allow regular (original formula) Sudafed tablets. No way, no how. (There seems to be a work-around using a compounding pharmacy, to get better "dilution", but we didn't bother checking further.)
But there were two different agencies we needed to contact.
What we did that time was just send an email stating what meds we were each planning to bring, what quantities/how many days/etc.
They wrote back listing the restricted meds, telling us when we needed permissions and in a couple of cases that we'd be exceeding a max. (Since we both take a lot of the same meds, we just made sure that between the two of us, we had "enough".)
We always have original labeled containers, and we've switched many to tiny ziploc type bags, with a new label attached. Then the air can be pressed out, and they can just be layered.
And we have copies of all scripts, plus a letter from our physician(s) stating that the <name of med> is required for medical purposes. Special mention is made of an injectable. We also have copies of everything in the cloud, just in case the paper copies get misplaced.
We just keep that same packet and take it on each trip. After a few years, we get fresh copies.
Perhaps because we are starting to look more and more like "Early Geezers" (!?), most times I've started to reach into the bag, saying, "I've got all the documents right here...", they seem to smile and wave us along.
but it's better safe than sorry!
For any airports where we stayed airside, we had the same ready, of course.
[There was one connecting airport where we would have liked to have a quick tour of the nearby area, but... there had recently been some nastiness with a tourist arrested, jailed, and held, though it seemed all was *not* 'right'. Still... we stayed in the airport. The penalties can be dramatically harsh in a few places, should things go sideways. Thank goodness for decent (!??) transit hotels these days.]
We joke that having all the docs/etc., is sort of like carrying an umbrella. Then it won't rain
GC