Hospital lighting stinks, plain and simple. Can you get to a window? If so, often the best option, if available.
Try to avoid up-the-nose shots...not the most flattering angle.
I've been tinkering with my own hospital shots to see how to improve them - the poor lighting plus the baby being either too red or too yellow (jaundice) or both(!) makes for some really funky unnatural tones. I gave up on fixing the coloring on several and converted to B&W to eliminate the problem which saved a few otherwise iffy images.
He's a cutie - congrats, Uncle!