I had a c-section and my lo was taken to the nicu. It sucked but they had beds in the nicu for parents. Not that I could lay on them. I tried once and couldn't get up. But I held my Lo almost constantly. I think I slept 45mins in the first three days not counting the knock-out for my section. The nurses laughed at me for dragging my IV and catheter bag accross the hospital to the nicu everytime my Lo woke up.
back on topic...
even under those circumstances, i would snooze with the lo.
I'm sure you'll figure out the best thing to do!