Nanny pay rate

Autumn • UO💛
Hey guys,
I've just finished my first month of nannying full time (40 hrs/week) for a 6 month old baby. 
I had babysat for the family before and they payed me $12/hr for that work. 
So, I got my paycheck for two weeks of working today- and it was only $550... That's less than $4/hr!!!! 
I contacted the mom and was professional, I just asked her what the hourly we agreed upon was, and she said it isn't hourly, its monthly. 
Do you guys think this is right?
I don't know what to do. 
I don't want to leave them without help, but I'm also working a job where I'm making significantly less than minimum wage ($9.75 in my state), full time, plus 1.5 hours transit each way... 
What do you guys think of this situation?
---------Edit---------
They want to make it a nanny share, so I would make about $12/ hr for two kiddos her age. 
Do you think that would make it fair?
ALSO- they have another nanny already in a nanny share who watches their 2 year old and another 2 year old. Is it okay to ask her what she makes? 
This is my first real job, I'm only 18, and am on my gap year before I move away for college.