The doctor gave her some medicine.
The doctor administered some medicine to her.
'Prescribe' has a different meaning according to http://www.ldoceonline.com/dictionary/prescribe
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'.
See below.Do you mean "had given" is incorrect here?
For example, 'The doctor had given her some medicine when she had an attack of asthma'.You need some other act in the past to use the past perfect.
Not necessarily.The doctor had already given her some medicine when she had an attack of asthma.
Is it OK now?