Should I come out?

I'm not sure if this is the right place to be asking for help, but I dont know what else to do. I'm really scared about coming out to my family. I'm a 16 year old teen who thinks they might be transgender. I was born a girl, and am out to them as a lesbian, but I've been having a lot of thoughts the past year about wanting to be a boy, and thinking that underneath it all I am. This didnt used to be such a pervasive part of my life, so I thought it was some strange symptom of my depression, which worsened when my girlfriend left me. Since all of these events happened within a few months of eachother, I had been connecting them in my head. But it's been the same regardless of whether I'm happy or sad at the time. I'll have phases where I'm okay being a girl, and some where I feel gender neutral, but then I have days, sometimes weeks in a row where I absolutely have to use male pronouns for myself at school, and I wear boys clothes.

My mother is getting suspicious. She knows I've got some issue with my gender identity, but I havent formally come out. She thinks the problems I'm having are a lot smaller than they actually are. I love my family and want to be open with them, but I'm scared of making a mistake. What if this is just a phase? Should I try to cope on my own and hope it gets better, or should I tell them? And if I do, how should I go about it?