I think she will probably figure it out when your stomach is the size of a water melon. Its a whole lot better that she finds out from you before she figures it out for herself.
Anyways, yeah, free clinic, or simply your regular doctor should see you on your own if you live in a place with free health care, I know as long as I had my medicare card, they didn't care how old I was or if I made appointments on my own.
You can probably get it done at a free clinic but honestly you need to tell your mom. She'll find out eventually and the sooner you tell her the less help she will be and the more she'll be able to help you.
just tell ur mom u cant hide it forever