is she crazy? my friend isn't talking to me because i told her we can't meet until summer.?

[Yellow]

Hi, i am socially awkward but that's got very little to do with my question (i think). I am an introvert because of which i don't hang out with my friends a lot. there's this friend of mine, she used to be my only friend once, she's really possessive and she's always telling me that she'll always be my best friend and all no matter how many more friends i make in life. if she sees someone write lovely messages (like i miss you or i love you or stuff like that) on facebook (from other female friends of mine) she gets really upset and starts asking me whether i have "moved on" and whether i dont consider her my best friend i know she's not lesbian but she's wierd. last summer i kept telling her that i couldn't meet her because i was busy with family and stuff but she would always get mad and say that i dont make time for her and stuff. i feel suffocated in this relationship, i try to send her fake "love you" "miss you" messages, but it seems really awkward. a few days ago, i told her that i can't see her until summer 2014 but she wanted to meet me in december holidays. and now she isn't replying to my messages, and 3 days ago i told her that let's meet up, but she still hasn't replied. she saw the message on fb (says "seen at 4:59pm") but she isn't replying. what should i do? should i forget about her? because she's depressed anyway and its mostly me who has to cheer her up and always be there for her. i feel like a therapist for her. on one hand, i don't want to be with her but i feel like she needs me (and my emotional support), she's just upset. on the other, i feel like she's making me depressed too so i should stay away from people like her (depressed). what should i do?