Question: What kind of fallacy would this be?

The mother's claim is not fallacious at all, she's merely warning her son of a possible danger. A danger that can be medically substantiated: See Energy-Drink Habit Sends Man to ER with Heart Problems via @LiveScience

The son however responds with several notable fallacies: Weak analogy. Non sequitur, a whole school of red herrings and an irrelevant goal or function. (A fallacy of distraction that irrelevantly critiques an idea for failing to do something it never intended to do) There's zero connection between the mother's warning about energy drinks to the son's aspiration for marriage.