I think you can say 'medicines' in plural here in English as well.
can I use drags instead medicines?
You mean "drugs" . . . You can use "Here are your drugs" but unless you are at a hospital or drugstore, that phrase could imply you are giving an illegal group of drugs to someone.
Why the plual to single switch?
Ліки is a mass noun. If you need to talk about any specific quantity you can say "(медичний) препарат" or "медпрепарат"
Ліки is a mass noun and is always used in the plural. English has words like this too. For example, bread and water are always used in the singular.
Here ARE your medicineS
I believe that "Here goes your medicine." should also be accepted --- just not sure if "Here go your medicine." is what would be the grammatically correct version --- is that what i got wrong?