A side effect is any effect of a medicine beyond the intended one. Some are trivial and temporary, some are useful in another context, and some are serious. Whether an effect counts as a side effect depends on why the medicine was given: drowsiness is a side effect for allergy relief and the point of the dose for a different purpose.
New, severe, or worsening effects should be discussed with a prescriber or pharmacist, and serious ones can also be reported to the FDA through MedWatch.