Should i give her some space?

here it goes...around 3 months ago i met a girl online and we really hit it off. i wasnt looking for anything more than a friend but i found myself so attached to her. i couldnt go a day without thinking of her and for the first month we talked nonstop. but lately it seems she doesnt wanna talk to me, and she intentionally doesnt reply to my messages. ive asked her if i bug her but she always says that i could never bug her....yet i feel i annoy her alot because she just doesnt wanna talk tome anymore. its always me starting conversations, she rarely is the one to say hi. i dont wanna break up but i want her to be happy because she is amazing and deserves the feeling i get when i talk to her, when she talks to someone. if it takes me breaking up to make her happy or some space and time away then maybe i should. please help. im 16 btw and im very insecure because ive had a sort of rough past relationships. am i being paranoid i wll get hurt again or am i too clingy?