I was told that the only medicine you can take without getting an AME's approval is water.
Everything else has to be run by one.
In real life there are some that people regularly use including some banned ones.
my experience is that some drugs will be veto'd by some medics and allowed by others.
I have limited personal experience in this area due to not having had to take much apart from antibiotics occasionally and decongestants (which I might add are the ones that some are banned but quite a few use)
And it also seems to be country dependant as well what they say you can take. Vick strangely enough is banned by some country's.