OP, congrats on hangin in there and making "it" work for you.
Many people will offer very different opinions here and no matter what, you have to look at what will work for YOU and YOUR family. Listing the accounts you have with limits and balances might help get you various scenarious.
I personally, would pay off my smallest accounts first. I'd look at each account that I paid off and say "one more behind me". The payments that went to that card could be applied to the next card on the list and so on. Even if you took half of the payment on the paid off card and applied that on top of the regular payment on the next card (give you a little more money for your pocket each month while still bringing down debt) it'll help. Others will say start with your highest APR accounts so you pay less interest. I've tried that myself, and while logically it makes sense, while you still have debt spread out across multiple accounts and just the balances decreasing little by little, it's not as satisfying or motivating to me as seeing an account with a zero balance. Just have to have the discpline to not use that card again (cut it up if you have to!).
Hi there - I totally agree with what KJM said in terms of using the "snowball" effect to pay off your credit cards. I'm guessing you work for the government as you describe COLA increases! Do you have MUD Days?
Anyway....I was thinking about claiming more each month on your taxes so that you do have more money coming in every month. This way you can use that money for your daily needs rather than credit-carding groceries. This way you can work yourself OUT of debt instead of just staying in the debt by using CC's to get by. I know you mentioned you did not want to do that - but that is what I would do in your situation - giving the government all that money with no return for you each month makes no sense, especially since you need that money and can pay off high interest cards monthly this way. If you get a 9500 tax return each year, that should bring in an extra $790 a month to use.
Good Luck! I hope your son is healthy and recovering.
PS: I am NOT financially savvy so take my advice for what it's worth. 
Being a single parent is very hard and I commend you for all of the hard work you are doing with your kids. I also hope that the medical issues can be resolved as the stress of worrying over a sick child can take a toll on your health, too. I know this first hand. I am raising two girls (3&6) without any financial assistance from their Dad. Carly, you and I are working on about the same budget. Dining out for my family is cheaper than full-blown grocery shopping. However, if you find you cans save by cooking at home-its time to make the switch. So, I will share what has worked for me. #1 list out all the credit cards that you have, the balances, apr, and due dates. Decide which one you want to use primarily and consider putting the rest in the freezer. (Really, when I had the high credit lines 8 years ago I placed my credit cards in water and froze them to keep me from using them.) #2 create a debt repayment plan and stick with it. MS Money has spreadsheets that can help you. You can google to see what's out there. #3 you may want to stop charging those medical bills. I have started asking the dr's offices to contact my insurance company to verify what portions I would be responsible. I have had success from dr's and dentists. After we agree to my out of pocket expenses, their office works out a financial agreement in which I also have them specify that they won't send a CA after me as long as I stick to the plan. #3 start saving some of your $9500 refund for your car repairs which leads me to #4 maybe your son could work part-time and pay for his own car. I started working at 15 and paid for my car note, insurance, and taxes myself. I learned the value of being a cautious driver since I was on the hook for any insurance hikes for driving wrecklessly. #5 you need to save for your retirement. You may not be able to pay for your son's college without saddling yourself with debt that you may not be able to repay. My parents divorced when I was a teenager. I worked/paid my way through my ENTIRE college career. At one point, I had three jobs. I wanted to go to school-my parents could not agree to who would pay for what-I took my education in my own hands. I paid my first 2 years of tech school and took classes that would transfer to 4 year schools. Then, I transferred to a private school for my higher degrees. IMO the first step to financial security is being realistic about what you can afford. Suze Orman has great books that provide help for any financial situation. My fav are Young, Fabulous, and Broke & The Laws of Money. Best wishes!!
