Most sump pumps do have a battery back up that is built in. Our house uses a sump pump and we've never had water in our basement, ever, so I don't think it's part of living in the midwest... My husband does check it every once in a while to be sure the battery is still good. (It's a light that he can see that indicates the battery is still good.)
I agree to ask a pro, but I've also heard that sometimes, the landscaping around your house can be a problem, such as how the earth around your house is sloping, etc. I would ask a plumber first, then see if he recommends a landscape guy.
This must be so stressful for you! I'm sorry that you are going through this, but I'd get a professional opinion about your house. Good luck.