I am a 19 year old who is going to start her first semester of her sophomore year of college this fall. Last March during the spring semester of my freshman year, my friend introduced me to one of her guy friends, who was an 18 year old freshman. He got my number, and we texted a lot over the next month. At the end of April, we both went to a party and then went back to his dorm room to hook up. The next day he texted me and asked if we could keep hanging out, so we started dating. I am the first girl that he has dated and he is the first guy that I have dated. I like hanging out with him and I am happy dating him, but a week after the night we hooked up he asked me if I would be his girlfriend. I told him that I thought we were moving a bit too fast and that I wasn't ready to exclusively date anyone right now. He told me that he understood and that we could "take things as slowly as I wanted to," but when he went home for summer break he told all of his friends and family about me All of my friends seem to think that this is normal, that it is great that he wants to commit this early, and/or say that they thought we "already were a couple," but this sets off an alarm in my head. He doesn't seem excessively needy besides trying to tie me down so quickly, but I still wanted to ask.
Is this something I should be concerned about, and how concerned? What other signs should I look for in order to determine if something is wrong and I need to break things off?