What should i do about my best friend?

Well i don't know if i should be her friend this is what has happened.Well ages ago she went out with this boy and then when she was going out with him she broke up with me and she had another best friend.Who was also her best friend when i was but i didn't like her because she was acting really weird.Then every time i hug her when she sees boys she pushes me away and calls me a lesbian.Then she broke up with that boy and we became best friends again.Then last month it was her birthday and she said i might invite you but im inviting jodie are friend and she said i don't think you to get along so im not inviting you.Then she said after her birthday i wish i invited you not her, even though im her best friend then she said we weren't best friend.I then said to her a few weeks after i want someone to tell every thing to about something and she said you can tell all your secrets to me and i said well we are not best friends and she said well i want to be so i said fine. But maybe she just said that because she wants to know all my secrets.Then at school in p.e i asked her best friend if i could go with her as partners and she said yes.Then When it came to it she said sorry i forgot she asked my first ( my best friend.) this morning before you.But they were lying and she even told me that after p.e. Then after that her and her best friend broke up and maybe she just wants me to be her best friend so she can have a best friend and she gets really jealous because her old best friend had a new one but they were just friends.Now this month it's my birthday and i invited her but then my friend came and told me ( her old best friend) that she said to her that her mum wouldn't let her go because she was staying at her dads (her mum and dad are divorced) but she said that when i had my birthday last year.Then when i was on the phone to her the other day she said her old best friend said to her (i invited her to) im not going if you don't go and she did the same thing last year to because my best friend wasn't there.I really don't know if i should be her best friend.Someone help me please.