I found out I was getting paid less than my job told me I was going to be paid hourly and when I brought it to the managers attention she said they can change the pay to what it should have been but she doesn't know about me getting back pay. I was wondering if I'm owed back pay because that was their mistake?

Yes of course you are owed back pay. How far back?
The manager may not know labor law, so don't get worried until you talk to personnel. Hopefully your company is big enough to have someone who knows what they are doing?
Don't be wimpy about this, but try not to be angry either.
Answer back if you don't get paid in a week.

Do you have any proof of the wage you were hired for? How long did this go on for? This is one reason you get a paystub. You are responsible to review your paystub and report any problems. If you didn't do this, you may not be entitled to back pay.