Not sure what the requirements are these days to take your boards and become a licensed cosmetologist. Back in the day, MD required 1750 hours (I think) of instruction - it's less if you just want to do nails. You learn hair, nails, cosmetic application and take some chemistry. You will fingerwave dummy heads until you're ready to kill someone. You will be better at it than your teachers - the old saying, "Those who can, do. Those who can't, teach" was born in beauty school.
By "nails" I mean manicures - nail tech is a separate profession and it would be worth your while to take the extra schooling and get licensed in that, too.
The type of pay situation depends on the shop. Some let you rent the chair and you keep whatever you make - if you're good, this is an incredibly sweet deal. I think the $8 haircut places pay you an hourly plus tips. Other shops have a different setup.
You probably won't get benefits BUT do you really need them? Think about it - unless you have a pre-existing that requires regular medical care, you're better off buying a catastrophic plan for $50 a month and paying your own medical bills. That way any major medical is covered, just not routine doctor stuff.
As someone who made a major career change in my early 30's (with two dependents, no less) the WORST thing that will happen is that you'll have to get another job. Big deal. As a single mother, you can also get a Pell grant or something to help you with your tuition costs.
You have nothing to lose. I say go for it!