Hi A.!
My daughter is three months and it wasn't until this month that she started sleeping more than 2-3 hours at a time- she is nursing. It IS exhausting- I have had 5 children, and with the fifth I think it is easier, because I know what to expect, but it is also still royally exhausting because I am older, have other kids who STILL wake at night, and a full schedule throughout the day that sort of x's out naps. I believe you said this was your first- I will tell you some things I wish I had known with my first.
Keep the baby out in the room you are in during the day, even if that room is noisy- and make sure it is well lit. More than likely the babe will stay asleep, but mentally it will start to program her to light and dark with her sleep cycles. Also, set an alrm to feed her/him every two-three hours during the day starting at 6-8 am until about 10- 11 pm. Both breasts, or as much of a bottle as she/he will take, and talk and play with the baby when they are alert. At night, if she/he wakes hungry, feed him/her, but keep it dark, try to keep it quiet(not playtime, tv time etc) Start a routine with the baby too, while she/he is still small - it is hard at first to set up- but if you set an alrm on your cell phone to go off when it is time for bathtime, feedings, etc etc. whatever works for you to keep you on track, then use that.:) I haven't felt like I have it some what together until my babies hit about a year old- so give yourself time to rest, learn your body after baby, and what will work for you and your family structure. It takes time- for baby. for us as moms, for our routine. With my fifth- she is three months and I STILL feel like some aspects to having a newborn is overwhelming and new. Basically, find what works for you, and abandon what doesn't. Everything you are experiencing is normal and exhaustion is something that doesn't quite go away completely, and takes time to get used to functioning around.
Feel free to email me @ ____@____.com. I went back and read the advice of the other ladies- the baby sling is GREAT- it did make my back sore, but for short periods of time it works wonders for a baby who likes to be close. Also, I cosleep with my babies, and that helps with sleeping through the night- ALL my babies hated sleeping alone- I went from cosleeping til three months, to putting them in their own beds AT three months once they fell asleep, to putting them in their own beds at six months etc. So a lot of great ideas from a lot of experiuenced moms- so much wisdom in one place- I wish I had been as lucky as you in finding this site when I had my first! God bless you!