There is nothing wrong with the word 'drugs'. It's not swearing or offensive. Instead of saying 'no, you should not use this word' your teacher should have explained why it might have problematic connotations sometimes. 'Drugs' is the commonly used word to describe illegal narcotics, like heroin, cocaine, crack etc but it has other uses outside of this. If you're going to a pharmacy it's obvious you're not referring to those types of drugs. If you want to avoid any misunderstanding then I guess you could use the word 'medicine' because that only has medical connotations. People don't take medicine for recreational purposes. A common way to say this would also be 'I went to the pharmacist to pick up my prescription.' The prescription is the order of drugs or medicine that the chemist makes up for you to collect.

It's not swearing or anything. No one will be offended by the word "drug". Without context it can refer to hard drugs, like cocaine, heroine, meth etc., but there's enough context here that it obviously doesn't mean that.

No, there is nothing wrong with it. However if you say "I take drugs- I do drugs- I am going to get some drugs" people will think you mean illegal drugs. So make sure you say "I take a lot of drugs for my medical condtions" or someting like that. Never say :I do drugs ( that is always the illegal kind) "I'm out of my drugs, I'm going to the pharmacy (chemist in the UK) ." Is fine, though we also say "I'm going to get my perscription filled."

"Drugs" is ambiguous; you should probably use either "medicine" or "narcotics". Medical prescription for marijuana, perhaps? Uncommon nearly everywhere, that.

Do what your teacher says, of course. However... "Drug" is a perfectly good word, but it refers to both legal and illegal drugs. I take several prescription drugs. I sometimes use over-the-counter drugs like ibuprofen. I don't use any recreational drugs. In the United States, most people, in everyday speech, call a pharmacy a "drugstore." But in order to avoid any misunderstandings, most drugstores now call themselves "pharmacies," and some people prefer to prescription drugs as "medications." The official Medicare website talks about "Drug coverage (Part D)," "Enter your drugs," etc. so it is definitely not a bad word. On the other hand, if I were coming back from a trip and a customs official asked me what was in my toiletry kit, I would never ever ever use the word "drugs." I might say "my pills" or "my prescriptions."