hi B.,
You are not alone. My baby girl is 9wks old. I feel the exact same way. You brought me to tears because that is how my life has been for the last 9 weeks. My baby went through a 3 week period of only sleeping an hour at a time, I was a basket-case. I have spent so many nights sitting up right on the couch with the baby in my arms.
My mom, my sisters and my best friend tell me to sleep when the baby sleeps, but I can't shut off either. It is hard, but you have to sleep. I know, you feel like the laundry needs to be done and the dishes are sitting in the sink.
But, last night I starting getting a sore throat (my sister is sick) so it hit me that I can't get sick - I needed to get sleep so I'm well. So I only woke up when the baby woke up at 4am, 8am, 10am and 2pm (she has colic, it took me from 7pm to 1am to get her to sleep). The dinner dishes were still all over the kitchen and my laundry was still piling up - I didn't feel guilty. I actually feel rested today.
Do you have family nearby to help you? Take all the help you can. It is so hard having a baby, I know I needed and still need support from my family.
I'll tell you what my friends tell me, Keep Your Chin Up, It will Get Better....
E. C