With the current circumstances as they are, you would be hard pressed to get a loan for a house at this time.
Like others have mentioned: pay your bills on time to increase your credit score. (or his, or both of yours).
It would be VERY helpful if you got a job. Even if it is a part time job. Find other moms with whom you can watch their child when they work so they can watch yours.
Do not go to a bank to borrow money. They only have limited "packages" to offer you. A mortgage BROKER has many more connections on finding you the right borrowing product that suits your needs. There are very low interest/down payment loans available to first time buyers. So, do your homework, find out what you need to do to get what you want and then make that your goal.
Now a days there are utility companies that become part of your credit history, so pay all of your bills on time and you will have a better credit score.
NC is a beautiful state and to find a home for 44K is almost unheard of, so do whatever you can to get what you want. Good luck.