Sentence Correction

Is parallelism the only criteria for this sentence

Not really, although it's very efficient to cut through the other answer choices. I looked at like this:

Only A or B can be right. C and D are awkward constructions, E is an independent phrase, and in order to use that one, you would need a semicolon, not a comma. B is wrong because it changes the meaning of the sentence slightly -- "having been prescribed" is different than "having a prescription".