Forgive me, I am going to assume you are young only because I can't picture an older woman saying "kissing and other things you do in private".. Rather, we have and do have sex and he comes over etc.... If I am wrong, sorry.
Also, sometimes "boys" are scared of introducing a "girlfriend" into a mix, if others are all still single. Can you tell us a bit more?
3 Months is not a long time but, I would want a date by then for sure, it doesn't have to be public/public but it sure does show someone has feelings doesn't it?
I would personally stop "and other things" allow the kissing and see if he nicks off or continues to see you
That's often a goood telling sign.