Will this ever be over. Lgbt?

I am currently going mad over this librarian that i had been crushing on for at least a year. however lately she started to notice me like staring at me and loads of eye contact. i don't know if she is a and i don't know what to do i braved it on one occasion and approached her however when she saw me she just stared at me i couldn't speak and she didn't either so i walked away. now now i have written like a letter to her which i plan on giving her one of these days,my best friend thinks i shouldn't i signed it secret admirer so what do you guys think should i give it to her and does it sound like she might like me?