I strongly encourage you to start taking the Prozac RIGHT NOW. It really takes a while for the drug to get in your system, then to know if it's the correct dosage or drug for you.
I struggle with a depressive disorder, and was very concerned about drugs when it showed up again with the birth of my daughter. I spent an entire session with my psychiatrist discussing the research that has been done with antidepressants & breastfeeding. The ones with the most research done that have shown to have no negative effects are Prozac & Zoloft.
My psychiatrist assured me that the amount that does get into the milk is so minuscule that it does not effect the baby. It's not like caffeine from coffee or something. It works differently.
You should definitely discuss your concerns with your doctor, but I do encourage to take action immediately. Depression can be crippling....especially when coupled with lack of sleep. You need to take care of yourself. And by doing so is also the best way to take care of your son.
Good luck, and email me if you want. You're not alone. Remember that.