Should I try once more or not??

Hi
My relationship story in brief:
I had a crush on this one girl in High school. She also had a crush on me our love between each other was growing.We hanged out together and flirted and the time came and I was ready to confess to hear that i love her. But when I found the right moment and I wrote to her on FB chat that I want to talk to her about something important. She didn't reply. And from that day onwards she doesn't talk to me.At first she started to avoid me at school.So I backed off and gave her time.Then after some time she started to flirt with me again. for a few days.I also flirted with her.But didn't tell her I love her. Then suddenly I became for her like a "Ghost" to her. For her I was not there she walked passed me without even saying a single word and didn't look at me (before she always looked or seemed more like she stared at me in class always) she totally cut communication with me. So I decided to move on but I couldn't find anyone else to fall in love with because I still loved her. Then it was prom time and I found out that she is going out with some other guy. I decided to let go of her and move on with my life. So I started to forget about her but didn't manage to forget about her fully.So I went to prom alone without anyone. At prom I had fun with my other friends who are single and with other single girls. And I saw that my crush while she was dancing with the guy and was staring at me over his shoulder. She did that for the whole prom.
That staring made my brain a totally got mixed up signs. My heart didn't know if she still loves me and wants to be with me??
Could you advice me please .
what to do next??
Should I try again to get her back or not??
I thought that I could write to her in chat a letter. Please advice me if I should change something in the letter below or if I should write it or not write it??
Letter would say:
“ I know you are there and I know you are reading this. Look,I know I have done something wrong because you don't want to talk to me these days. I am sorry for whatever I had done wrong Please forgive me.”

Please advice me what to do next
Thank you in advance

This actually happened to me once :/ In your place, I would just let go of her, there are a lot more girls that are looking for a nice caring guy like you ;)

Whoa no! do NOT send that message, you will look like a sniveling weak ass fool. Girls get turned off guys that are begging, apologizing, crying whining, ugghhhh it's so unattractive. Another thing, never ever tell a girl your feelings when you are not even dating, they don't want to hear that crap. They want to hear the words, "You are so hot" " You are a turn on or You turn me on" etc. They want to feel sexually desired. BUT they also don't like a guy that makes a fuss over them either, or put them up on a pedestal. They like the challenge and to chase too.

You sir f'd up. Here's this girl flirting with you, and you didn't ask her out. Some other guy was confident enough to ask her out, so obviously she went with him. Do not communicate with her if she has a BF. Stop flirting with her if she has a BF. You must respect their relationship.

Options: Forget about her and meet someone new.

Wait till their relationship ends, and ask her out.

Be friends with her (which I would never recommend) monitor things.

you can always give it a second chance....

It sounds like a lost cause I'm afraid.. so she was staring at you but she was dancing with another guy. So um... if she does have any feelings for you, I mean that's a red flag right off the bat. She's not gonna be faithful. Let it go =/