Having surgery can be difficult enough. But to worry about paying, the household bills and taking care of your children, is another added expense. Check and see if you have disability insurance. This would give you, a paycheck while you are out. The money is not as much, as your normal paycheck, but at least it would be something.
You might also be able to collect unemployment temporarily. If this or temporary disability does not work, call your utility companies and let them know what is going on, they may be able to help you out. Also contact your food stamp office and see what they can do, they have temporary help services as well.