This question borders on "what to write" instead of "how to write", so I will concentrate on the latter.
If your character has masturbated, he has had erections. Probably every day, since teen age boys do. If he is "reserved" and doesn't like to think in crude terms, then he will have invented his own words for this phenomenon.
Changing "masturbation" to "catharsis" is focusing on the emotional result instead of the activity. I would focus on a similar language transition for an erection: Focus more on the emotional result.
I think "tight trousers" is a cliché, and doesn't really convey what the character is feeling. It is also not entirely accurate, men and boys can wear brief and keep their penis angled down, in that case they can have an erection that doesn't show. Most boys figure that out early, and don't "pitch a tent", as the slang goes.
Also, erections are not all or nothing; they can vary from "chub" to full staff, depending on the level of arousal. For somebody in a bosom hug, I wouldn't assume a full and raging erection; I'd guess the boy had the beginning of one, a partial erection.
Were I writing, I'd focus on the emotions this causes. Between males and females, I'd guess the frequency of unwanted or inappropriate sexual arousal is higher in males, and the sensations may differ somewhat (although engorgement and increased sensitivity are common to both genders), but I'd also guess the emotions of unwanted or inappropriate sexual arousal would be similar, and by focusing on those we can cross the gender-gap.
I also wouldn't try to summarize this in a word or two; if this is an infrequent occurrence in the story, you don't need a shorthand. Allow yourself a sentence or two, to convey the feeling accurately. Remember, readers don't mind reading.