Is the friendship worthy it or i should just quit?

Okay so i've been best friends with Lucy for a long time now so she should know what i like and what i dont. I really hate it when someone talks about me & my secrets behind my back. A few months ago something serious happened in my family and of all my friends i only told her about it and i told her thats my secret. She has this cousin she kept talkin abt but i didnt know her until like 3 weeks ago. So far we are getting along well and we're bcoming really good friends. The other day her cousin asked me about the family story that I told Lucy not to talk about to anybody and most of my other secrets. I am so upset coz i trusted her but shes been talkin abt my secrets bhind my back. Right now i dont know wat to do cuz I've lost trust in her. Should i continue being frenz wit her or i should just quit cuz it'll be no use havin a best friend who is so untrustworthy?