I like her a lot but not sure if she is confused or what? Can we be freinds?

have a hard time to get over her she is in my mind the whole time for an year now. Whenever something bad happen to me i just think about her or open her fb just to look at her and i feel better. I never get attached to soemone this much even though i dont have her number and never went on a date. I feel im crazy and I've been denying my feelings but i think im in love with her. And i just feel stupid.
we were attracted immediately from the moment we met and she flirted back. I came back to her many times until she opened up to me and started to try to talk with me i know that she is extremely shy especially with me. Anyway i saw her flirting with another guy and playfully touching him and I ran away. At first she seemed shocked then she started to try to get my attention but not talking to me. Then i felt guilty went to her gave her a gift a cup for her new office she was defensive then she started to act sweeter than before staring at my eyes smiling. She even tried to use my cup in front of me like she was happy. I told her i would be back and told her the day and time then i didn't then i went to her but i didn't see her like she avoided me and she went on vacation. Then we both started to avoide each other and she kept having this looks when she see me at the street like she doesn't know what to do.. Then i found out that she is dating a guy but she tried two times to get my attention so i ignored her. After few months she followed me one day walked close to me when i sat down she looked down like she wanted to talk then she left. Then she did the same before my vacation she came to where i work acted busy sat and gave me her back doing papers then she suddnely stood up and looked at me across the room i looked away and she did the same. I don't understand whats going on with me and her i never been this confused woth a woman before i used to know if they want me or not but with us there is this stupid push and pull and i feel like im going crazy?
I thought long and hard and since she is leaving work soon is it okay if i go to her and give her my number and ask her to be freinds?????

 

Thank you so much for giving me some insights
I really regret few things ive done with her i let my fears from the past control me...
And its right i only feel obsessed and angry now but to be honest she was the first person in my whole life who gave a shit about me without wanting anything in return and she doesnt know that what she done for me was so special and deep and she helped me a lot which make me feel upset if we ended up like that with no clear ending... I would be a good freind for her because she accepted at my worst and that was enough for me to know that she was a nice person after all...