K.S.
I am so sorry that you are in this situation. I became a single mom before my kids turned 1 and 3. I know how you feel and how overwhelming it can be, especially when they are so young. One of my favorite resources when I needed a few hours to myself was the drop-in daycare centers. They can take kids up to three or four hours at a time and there is no need to call ahead. It is a little more expensive than a regular daycare but it is great when you want to just go shopping by yourself. I would also use this when I wanted to spend time alone with each of my kids. My other favorite thing was online grocery shopping. It cost a little more but it was sure better than dragging two kids through the store and then trying to carry all those groceries into the house.
As far as sick kids and other unexpected situations, I would look for a college student that may be able to do occassional babysitting for you. You could also check with your local hospitals to see if they have a sick child service during the day. I just got a postcard in the mail the other day from someone who is starting a business babysitting for sick kids, so you might find something similar in your area.
Good luck and stay strong. I know it's tough but it does get easier. Just remember to take care of yourself first. Feel free to email me if you ever just want to talk.
K.