You don't wear underwear under cycling-specific shorts because they have a cushioned pad in them that's designed to sit against your skin. If you wear underwear, too, things supposedly slide around too much and chafe. (I say "supposedly" as I've always just followed the advice so I've no personal experience of the effects.) Non-cycling-specific shorts don't have the pad, so there's no particular reason not to wear underwear with them.
Consider how far you've already ridden that bike in one go and how you felt after that. When I got my road bike, I started riding in regular gym shorts and that was fine for me until I started riding about 65km, at which point the hard saddle made my butt ache enough that I went out and bought some proper cycling shorts. However, that was just the tipping point where I decided to get the proper gear. 65km got a bit uncomfortable so I spent some money to avoid that. It's not like I was in pain or dying or anything so I'm pretty sure I could have done 75km with nothing worse than discomfort.
However, for commuting (5–25km, depending on what route I take), I still just wear the gym shorts, because they're completely fine at that distance and nobody in the office needs to see me in MAMIL* mode.
Long story short, if I was going to cycle 75km, I'd prefer to get some padded cycling shorts, but I'd be OK in gym shorts. You have a different butt on a different saddle and possibly different financial priorities.
* Middle-aged man in lycra.