My baby was born in January too and she also only sleep for 3 hours. She was fed at 21h00, 00h00, 03h00 and then 06h00. And lately she starts to have 4 or 5 hours of sleeping and someday she will sleep for 8 hours like us.
One tips we did in order to avoid exhaustion is to sleep as she sleep. So we could rest for 3h 2 or 3 times. Sure it's not like resting for 8h but it helped.
I found this letter from (NHS Ayrshire Maternity Unit) that gives us some strengh and comfort.
Dear Mummy and Daddy
Please keep this letter from me in a place where you can read it and re-read it when things are rough and you are feeling down.
Please don’t expect too much from me as a new born baby, or too much from yourselves as parents. Give us both six weeks as a birthday present, six weeks for me to grow, develop, mature, and become more stable and predictable – six weeks for you to rest and relax and allow your body to get back to normal.
Please feed me when I am hungry, I never knew hunger in your womb and clocks and time mean little to me.
Please hold, cuddle, kiss, touch, stroke and croon to me. I was always held closely in your womb and have never been alone before.
Please forgive me if I cry a lot. I am not a tyrant who was sent to make your life miserable, the only way I can tell you I am not happy is with my cry, bear with me and in a short time, as I mature, I will spend less time crying and more time socializing.
Please take the time to find out who I am, how I differ from you and how much I can bring to you. Watch me carefully and I’ll tell you things which sooth, console and please me.
Please remember that I am resilient and can withstand the many natural mistakes you’ll make with me. As long as you make them with love, I cannot be harmed.
Please don’t be disappointed when I am not the perfect baby you expected nor be disappointed with yourselves when you are not the perfect parents.
Please take care of yourself; eat a balanced diet, rest, and exercise so that when we are together, you have the patience and energy to take care of me. The cure for a fussy baby is more rest for Mum.
Please take care of your relationship with each other. What good is family bonding if there is no family left for me to bond with.
Keep the “big picture” in mind. I’ll be like this for a very short time, though it seems like forever to you now. Although I may have turned your life upside down, please remind yourselves that things will be back to normal before long.
Enjoy me – I’ll never be this little again!