As ems said, we need context before we can tell if the tense is OK, but the verb is fine. It's vague enough to cover prescribing it, handing it over, and pouring it down her throat. It's very common indeed.
People outside the medical and legal professions don't normally use 'administer'.
Yes, you are right regarding the need for context. My question was about whether the verb "give" is used in such context. Do you mean that all of the verbs below can be used when we are talking about a dr?
The dr gave her a medicine,
The dr prescribed a medicine, (does it have different meaning?)
The dr handed medicine over (what's the difference between gave and handed it over?!)
The dr poured the medicine down her throat.
I'd appreciate if you let me know the difference between these verbs.