I agree with the above answer: Nobody should tell you what to do, though advice and listening to what other people say has its value. Just remember that in the end it is your choice.
Maybe its just how we see it in my culture, but I would certanly not call "making out" and "texting other girls" the same as being unfaithfull. To me being unfaithfull is eithr falling in love with someone else, or engaging in sex with someone else.
Texting or maing out when drunk is not a good thing to occur in a relationship, but it is pretty minor stuf in my book. Conflicts over such stuff (and more major stuff too) are a part of most relationships and may occur from time to time. Normal conflicts in a relationship can and will occur, just make sure this is not becoming an abusive relationship. Rule of thumb is: are both paties in it by their own free will and nether feels forced to do anything? If so, then it is a healthy relationship.
I imagine the reason why incidents like the texting thing or the make-out thing occured is because neither of you is yet convinced if your current relationship is really this big serious, long-term potential thing.
So you have two ways to go as far as I see it:
9 month is some time, but it is certainly not half-of-your-life either. Perhaps the best thing is simply to give it more time. Take it slow. See where the relationship leads you. If you do not feel pressed for time, then why not wait until you or he gets naturally into a point to make some big decision.
On the other hand, if the pressure is becoming unbearable for you, if you feel that now is a time to make up your mind and that waiting more would simply not be possible for you, thn bring this up. Talk to him 1 on 1. Explain how you feel, do it clearly but not in a way that would make him feel attacked or make him assume that you are only accusing him. Tell him that if the relationship is to become more serious, there are commitments that have to be made and some "do not cross" lines that need to be drawn up. If the texting thing is bothering you a lot and is interfering with your relationship, thn tell him that's one of th things that needs to stay "outside the do-not-cross-line".
Keep in mind this talk might have varying results and in the worst case scenario he may decide that he doesn't want to be in this form of a relationship that you are proposing. You guys ned to talk this over, be flexible and get ready for possible compromises. Nobody built a good relationship by trying to be a dictator.