Not sure what to make of this situation

So I’ve been talking to this guy for a little over a month and things have been getting kind of serious but we don’t have any labels. He shows me off and treats me like his girlfriend and I treat him like my boyfriend but it hasn’t officially been that. Do you ladies think it will turn into something or will it keep being like how it is now?? School is also starting in two months so I will be able to finally see him then if I need to make a move.