I'm sorry this happened. Luckily you have caught it before it affects you later in life.
I had something similar happen to me, but it occurred once I turned 18 and began to receive credit card offers in the mail.
I left for college and got a part-time job. I would sometimes come home on weekends, but that's about it unless it was a holiday.
After college, I applied for a credit card and began using it. I mentioned this to my mother, who seemed excited about it. She asked how much the credit limit was and commented that "the one I got you when you turned 18 has a much higher limit than that." Perplexed, I asked what she was talking about, since I had never used a credit card prior to being in my early 20s.
She spilled the beans that she had responded to the credit card offers that came in under my name. A couple had pretty high limits, but the remaining six all had $500 limits. She had maxed out all and was making minimum payments. Apparently, she was using them to purchase items online (which wasn't really much of a thing back then) and via catalogs.
I was pretty upset, but she reasoned that she was helping my credit by doing this and that my parents were making the payments on the cards, so it didn't matter anyway. I don't know why, but this made sense to me so I let it go.
Fast forward a couple years. I get married and we begin contemplating getting a house. I check my credit and to my surprise there are the eight credit cards that my mother had signed up for and all are maxed with very spotty payment history. It was almost like they'd only make a payment on one each month.
I was furious and had a very adult conversation with my parents, which I probably should have had when I first discovered what was going on. I wanted all information on all cards that they had under my name. I had all of the account numbers changed and updated the address to my current address. I also removed all other authorized parties from the accounts.
For me, pressing charges wasn't an option. I really hated what they had done, but they were my parents. I just couldn't bring myself to doing anything else.
I had to empty my savings just to get the credit cards down to tolerable levels where I could afford the minimum payments each month. Slowly we began to pay off each and close them. It was very hard on the relationship with my wife, but we got through it.
As a result of all this, we weren't really credit-worthy enough to purchase a home until our early 30s. It really set us back a good five to six years on where we wanted to be. I also don't speak to my mother any longer, and the relationship with my father is not that great either.
It was a rough situation, and I hate seeing anything similar happening to other people.