need help becoming friends with someones im not really friends with anymore?

so when i was like 4 years old i was friends with this girl but we ended up going to different schools so me and her didn't really talk any more but now high school came around and shes going to the same high school but i think i blew all chance i had at becoming her friend again. okay so closer to the beginning of the year she said and to me and i said hi back not knowing it was her and we didn't really talk to each other but then i found out it was her and i sayed hi to her asked if she was her then didnt have anything else to say so i walked away (note this was like 2 months after she definitly knew it was me.) i then two weeks later asked if we could hang out at lunch that day. she sayed no because she had friends to hang out with. i feel like an idiot for doing it. i have had chances to talk to her again after this but i didnt use them because i feel like she doesnt want to be my friend or something idk let me know what you think and anything that you think i should know to become friends with her again