I would tell your mw as you might be anaemic, they can at least rule it out.
IMO i would say just get use to it, a newborn needs to feed every 3/4 hours round the clock and could take upto an hours each feed. That leaves you with 2 hours to in which to eat, drink, change the nappy and wind the baby.
If you are breastfeeding it can be every 2 hour feeding. If you are expressing, breastfeeding and toping up with ff, it will take longer and i think i worked it out as 8 hours in every 24 to eat,sleep,drink and get dressed/showered. Add in a toddler, the school run, cooking meals for family, housework and childrens after school activies and it does not leave you with much time to sleep.
Luckly the baby will grow up and it will get easier but the sleep depravtion is accumative, so get as much sleep now as you can.
With my first i got sleep insomina in the last trimester 
Good luck
ps sorry for spelling mistakes i'm dyslexic.