"Medical research" is not, per se, subject to IRB regulations so no part of that law defines "medical research". However, 45 CFR Part 46 is how one arrives at an answer to the question of whether institutional review is required. You primarily must determine if the research on human subjects is
conducted, supported, or otherwise subject to regulation by any
Federal department or agency that takes appropriate administrative
action to make the policy applicable to such research.
The definition of research in fact could exclude certain actions that look like "medical research", because of an exemption that
the following activities are deemed not to be research... Public
health surveillance activities, including the collection and testing
of information or biospecimens, conducted, supported, requested,
ordered, required, or authorized by a public health authority.
If the questioner was authorized by a public health authority as a form of "health surveillance", the question is not research. Also, §46.104 defines various forms of "exempt research". The main point here is that it does not come down to "defining medical research", it comes down to specifying whether the research is subject to the IRB approval regulation.
In that section, in (d)(3)(i) there is a real possibility that the question is not subject to the IRB requirement. There is an exemption for
Research involving benign behavioral interventions in conjunction with
the collection of information from an adult subject through verbal or
written responses (including data entry) or audiovisual recording if
the subject prospectively agrees to the intervention and information
collection
subject to one of three criteria that define "no risk" (anonymous, would not harm the subject if revealed, or is subject to a 'limited review').
However, the condition you set, that the question is asked by the person who administered the drug, changes the practical outcome, because the "asking a question" part may not be regulated, but the "administering a drug" part could be. It is when a drug manufacturer conducts tests on a new drug and the survey is part of the efficacy and safety review. It is not when your doctor suggests that you take two aspirin and call him in the morning to report any adverse effects.
The other thing to bear in mind is that institutions can impose requirements than are more strict than are mandated by the law, as a precaution.