Would you go for a hot tub/sauna “date” with someone you’ve only “dated” 3 times?

We’ve been talking online since February and met for the first time mid July. He’s a good guy, I trust him a lot. It’s not that I’m afraid to go, it’s that I’m not ready for such things. It’s too exposing and we’re not even a couple or anything to do such tasks.

I get it, he’s trying to make me relax from the university stress, but he doesn’t realise that I’m not comfortable.

My question is, is this a normal task to do with someone? Am I overreacting? Should I go? Or am I right not feeling like going (even though I’m 110% interested in the guy). I said no many times now, and he doesn’t seem to give up on me.

Ps. The reason I don’t want to go is not only that I’m not comfortable yet, but also because a health issue I’m experiencing for some months now and have never mentioned anything to him. I’m experiencing symptoms of anorexia and have lost lots of weight. I get dizzy and nauseous very often, I force myself to eat a single meal per day. It has gotten pretty serious lately, but I really don’t want to talk to him about this. I’m really insecure about it, I’d hate it if he knew.