Is it normal to want to rid your life if a jealous friend?

I have a good long time friend who is jealous of me and I think she takes it out on me to make herself feel better. She has never been supportive of me and doesn't give me compliments because she resents that people think I'm pretty. Then, I got into and decided to go to the college that she wanted to go to. It's been my dream scool for years but we went on a trip to see it and she fell in love with it and she was rejected. She started making excuses saying I probally got in because I'm a math major which she thought was less impacted (think again!). Then, I got a nice car because I'll have to commute to college. She flat out called me spoiled in front of our group of friends and said "the paint will just fade away in the sun". I messaged her saying that I want our friendship to work out but she can't insult or put me down when I've been nice and supportive to her. She called in tears saying that she was sorry and of course I forgave her but now she isn't inviting me to hang out with our group of friends. She got a car recently and she kept bragging about it but when I come out of my house, I cath her with her hands cupped to my window and peering in at my dashboard. I want to be her friend but I can't handle this insanity! She wants to come sleepover at my dorm when school starts but honestly, I think I need to distance myself from her. is it normal to want to get away from a good friend who is so unhappy and insecure? She's two sided- happy at once and then destructive and mean! Should I talk to her or just cut her off? is it normal to want to put distance between us? What should I do? I'd love some advice! :)