Feel for you, doorbell. You sound a bit like me before I got help. I got to the stage where I felt everyone would be better off without me. Finally I got the help I needed - in my case it was Citalopram.
OldMumsy speaks a lot of sense. Think if you have been on the prozac for a while you might want to have a chat with your GP/Practice Nurse, to see if there is something more suitable or you are on the right dose. In the meantime, just focus on each day. As your children get older, your horizons will widen again.
I think when you have very young children it's such an enormous transition from the world of work, where you are more goal-oriented. I didn't miss work so much as the regular feeling of achievement. Raising children isn't the same kind of work at all, and with babies and very young children it's often just bloody hard grind, unrewarding and thankless. I would often feel like a skivvy, and wonder what the hell happened to "me" the day my daughter was born.
It got better for me, and I'm sure it will for you too. Also, please don't worry about your children, they will be fine. The fact that you are worried about any effect on them means you are already protecting them.
Rhubarb, depression is not the same as just feeling a bit down and sorry for yourself. It doesn't help people to tell them to "quit moaning" and that "life could be much worse".