In addition to Michele S.
Yes, lack of sleep impairs the immune system and a host of other things. Sleep, is restorative and 'repairs' the body.
Now, can your Hubby do night-time duty? But since you are nursing... or, maybe at night, you can give a bottle of your milk? That way you can actually sleep/rest at night. That is what some couples do.. the Hubby takes over night time. Sure, the man needs sleep too, but when you have a baby, BOTH spouses have to juggle sleep/night duty.
AND, on weekends... this can be your "off" days. Meaning, have hubby help around the house, make you lunch, clean, and when your baby is napping, YOU nap too. Really. I know its hard to actually do it... but just rest and nap. Catch up with rest on the weekend when Hubby is home. That is what I did and still do. On the weekends, that is my 'break' (sort of), and Hubby takes the kids out. So I can nap. And I do. And my kids are on a regular nap routine, so it's easier to actually plan these things.
Really though, since it's about your health, it's important. A Mommy has to be healthy. Your Hubby can understand this I'm sure. Just sit down, decide on a 'schedule' and have him take over household/baby duties too. For me we have a "Daddy Do-List"... and on this list is the actual things that is my Hubby's responsibilities... otherwise, they forget and just think the Mom will do it all. It's just men. They don't think like us. So this helps. You NEED to delegate chores and duties. Since you have a Hubby and are not a single Mom, you have the privilege of having your Husband help. So you can rest.... or to have just a break. Moms need this. Or you will go bonkers and get more rundown... which will impact your health and just emotionally from not getting run down.
Try it.
Do not take over the counter meds.
Just some ideas,
All the best,
Susan