20 year old here, I got the same problem when im with my girl. I'm not sure she's noticed it yet since we've been intimate only a few times so far but it is a bit embarrassing when it's already kinda erect after just one touch or something. And I also get quite a bit of precum (after making out for like 4 hours it hurts), I find this more annoying tbh.
Anyway, I just think of it this way: Id rather have it like this then the opposite (not getting it up at all).