I think almost everymale has had an erection in these situations, specially at young age and/or with your girlfriend. But there's a big difference between exposing it openly or try to hide/reduce/disguise it, either running to the water, adopting a disguising posture, doing something to reduce it.
Even today I get aroused when I apply sunscreen to my wife, I just let the thing cool down (sometimes, she doesn't collaborate, she insists in applying sunscream in my parts).
However, many years ago I didn't stopped. I was 23 or so, and I was with my girlfriend in Es Trenc Beach in Majorca, a big -and then- wild beach with no buildings/hotels near it. You needed a car to get there. In was end of June, quite early in the morning, so very few people there. We got horny.
We went to the water to calm down things, however we couldn't. So we went more and more offshore -very clean and very swallow waters-. She was upside down crossed in a inflatable mat and I was pushing her and the mat offshore, she was with her legs open, and suddenly I was inside, and I couln't stop. We were at least 200 mts from the shore.
It wasn't a quicky one because the water was quite cold and this extended the action and anyway we went absolutely wild.
Fortunately, nobody noticed it or at least, nobody said anything (no children then, most of people were quite old because the dates).
Best day of the beach of my whole life.