Is this jealousy? What can I do about this friend?

I have this so-called "friend" that I thought was my friend. She's 39 and I'm 34. She goes to the same college I go to, but she is in the Nursing program already (RN) and I am still taking prereqs for it. I was accepted into the Honors Program of my college about 2 weeks ago, but I will start taking the rest of prereqs as Honors beginning this Fall. I told this "friend" of mine, and she was so happy for me at first. She was the one that had been telling me "don't go into the Honors program because it's harder, it's challenging, it's going to bring your GPA down, etc". So I went ahead, applied and was accepted into it anyway. Today she called me (she's always depressed, tired, frustrated) and said "How do I get into the Honors Program?" I asked her why she wants to join the Honors program, since she's got 1 year left to finish her nursing school (she finished all her prereqs). She said, well you're on it, I want to get on it too! I told her that when I first wanted to join it, she was the one that put me down for it, but now she wants it too! Her GPA is about 3.1 until now, and mine is 4.0. So she likes to compete with me. I am not worried about competing with her because 1-she's suposed to be my friend and 2-she's already into the nursing program and I haven't even applied yet. So what's her problem? Jealousy? Besides that, I am getting tired of her calling me often and being so negative, gossiping and complaining about people we know. I want to hang out with positive people. I am thinking about slowly distancing myself from her, but she's kind of possessive. What can I do about it?