Relationship Anxiety

I just got into a relationship with this guy I really like. And he’s a little angel but I have realised I have severe relationship anxiety. I overthink everything he says to me, every time he takes longer than a few hours to reply I think he’s ghosting me or fed up. Things like that.

Because we just started dating I don’t want to bring these issues up with him yet, does anyone have any advice to handle it on my own?