It sounds like you're looking at the USDA Direct loan based on your income so you should start there.
The USDA website has been down all morning so you'll probably need to try it later.
When you get on the site, go down the left hand side and click the contact link for the Direct program and find the office that serves your area.
As far as your credit goes, the # 1 reason your scores are not going up is because you don't have enough open/active trade lines in good standing. Anytime child support shows up on credit, it's a derogatory account so that's hurting your scores as well.
There may be things that are there that you don't understand.
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Our FHA loan will allow a middle score of 600 and higher. Scores between 600-639 require additional underwriting requirements .
May I suggest applying for a secured line of credit from Capital One or HSBC, If you belong to a credit union that report to the credit agencies, than take out a small personal loan.