What to think and do about my relationship?

I have been dating this girl for a year now and have tried explaining some things to her, but she still does not get it. She hovers constantly smothering me, and I have talked with her about this before. We have a lot in common, so don't get me wrong. I do love this girl. It is just the whole TOO "clingy" thing is driving me nuts. I like spending time with her, although sometimes it is a little much. It seems she has to be with me at every waking moment. I have tried to suggest her finding a hobby or making friends, but she always has some excuse. She is so overbearing it is pushing me away and I have told her about this. It is too the point she irritates me, causing fights and little disputes because "I have an attitude." I told her I need some space and the space she gave me was maybe an hour of alone time. We are getting an apartment together and I am afraid she is gonna get even more "clingy". I don't want her to go Lorena Bobbit on me and accuse me of cheating. It is like everywhere I am or she is, we MUST be together. It is really becoming too much. I know it is wrong and I don't know why I am thinking the things I am. But it makes me want to talk to other girls even though I love her and don't want it any other way. I even had a dream about cheating on her. In this dream I was playing with little girl whose mother was sitting next to me, while my girlfriend is sitting directly in front of me. The mother of the girl stands up and whispers in my ear, "Make me chase you." I tell to stop, that the girl in front of us is my girlfriend. She tells me, "It won't bother her" and proceeds to kiss me. She tell me her name which was like Lisa something and that I should look her up. That is when I woke up. It was a pretty vivid dream. The girl was pretty attractive: long dark hair and slender body. I woke up to my girlfriend and automatically, I admit had an attitude which I believe was a result of the dream. I have feelings of wishing the dream was real. Also when she does not get her way she gets an attitude. Especially relating to me choosing to go in a direction that does not involve her. She gets an attitude like she is made and that I am obligated to be with her no matter what even if it does not make sense. And it drives me up the wall and I try to explain and I only get a one word response like "Fine...". I really don't know what to do...I am about at the end of my ropes I guess you could say. Please help....oh and any incite pertaining to the female mind. I look around, she looks around, because she thinks I am looking at another girl. She looks around, I look around, and I obviously some attractive guy, so I ask what are you looking at? She says nothing or something random. I tell her its okay that it is natural, but she won't admit it. Only turn it around on me saying, "so what are you saying? you check out other girls!?!?" Makes me think she has a guilty mind....so again please help!