Debt and Credit (I Don't Know Anything, Advice and Opinions Appreciated!)

I don't know if anyone will know anything that might be able to help me, but all advice would be appreciated! By the way, a TL;DR is at the bottom for anyone who doesn't want the read the passage but can answer some questions relating to credit/debts.

About two years ago my family lost almost everything. My dad got sick and lost his job, our only vehicle was repossessed, and we relied pretty heavily on odd jobs like scrapping junk and babysitting to get by. I was about to head off to college but instead stayed behind to help keep our family afloat somehow. I took a babysitting job, that while underpaid helped a lot.

At this same time, my aunt decided to help by getting us internet and cable, which we presumed would be under her name/account with the local company. This went by for a few months until my aunt was unable to pay the bill. Suddenly, I started receiving bills from the company, and discovered that somehow she had managed to open the account under my name months ago without my consent or knowledge. Not only this, but it wasn't even in my real name, yet rather a nickname relatives call me.

I was confused and a bit furious, but at the same time I was working and my parents were making a decent amount, so my dad and I decided to split the bill. As I said earlier, at the time I was working as a babysitter from 6am-7pm every weekday, and the local company wasn't open during the times I was off. So, for a couple months this worked. My dad and I would each pay half, and because I worked I let him go in and pay the bill every month.

Then, suddenly our services were disconnected, and I receive a letter saying I owe 250$ in unpaid bills. We generally paid between 50-100$ a month, and I always put forth 50$. This meant there were at least 5 months worth of my father not paying his half, which was supposedly unaccounted for on the bills.. From the point I first got the bill, there was always a high balance on the statement stating we owed 200$+ every month, but every time we called their corporate office they informed us it was a mistake made by the local office and to only pay the 50-100$ we owed for the month. After we got our services disconnected, the corporate basically said that we owed the 250$ plus an extra 250$ for equipment. This means about 500$ in supposed debt.

Around this same time, I had hospital bills to pay and also lost my job, so I couldn't afford it. They contacted a debt collector, and now I've been receiving letters, mailed to my nickname, for half of the 500$.

I thought this would effect my credit a great deal, when when I've tried to check online for my credit scores and reports, they don't have enough information to create a report.

TL;DR
So basically, I'm pretty confused and looking for opinions. Is it possible for this to effect my credit when I'm pretty sure they don't have my social security number? Does the fact that it's listed in my nickname and not my actual name have anything to do with whether it effects my credit or not?

I also received a notice from a debt collector for 100$ worth of unpaid hospital bills in my real name, which I know is exactly what I owe, but wouldn't that show up in my credit stuff as well?

Also, I know nothing about paying back debt collectors. If anyone knows anything at all about this kind of stuff, or had an experience they think might be helpful, I would be so appreciative. So far I really hate adulting.