I have a 2-yr-old AND a newborn. The new baby is bottle/formula fed (wanted 2 nurse, didn't happen...long story about my labor/delivery, bottom line, new baby was a NICU baby, so they HAD to bottle feed her. I couldn't pump/nurse until almost 2 days later), so that is a HUGE help. My husband, mom, mother-in-law, brother, and other friends have helped with feedings. It's a Godsend to be able to bottle feed, seriously.
Maybe you could pump/nurse so you can bottle feed the new baby, or so that someone else can do a feeding? Also, when it comes to your older child not sleeping/napping right now, it could just be 'cuz the baby's taking over his turf. Have patience, be consistent, and hands down, sometimes U just have to let them get upset. They HAVE to learn that they can't get their way, and they'll waste energy trying SO hard to get YOU to bend anyway, so just let them wear themselves out. Also, there are times when the BEST THING you can do is NOTHING!
Your newborn could also be going thru a growth spurt (3 weeks, 8 weeks, 3 mos., 6 mos., etc.), so that could also be the reason why he's being difficult right now. There were a few times when my newborn would wake up crying, then after a few minutes, she'd just nod herself back to sleep. Go figure :)
Do you have any family/close friends who can just come over and play/babysit your older child so that you can focus on you and your newborn? If not, start looking into Mommy and Me groups (church, community center, library, local Barnes/Noble, etc.), and before U know it, you'll have total strangers as your closest friends. Do NOT be afraid to ask for help when you're overwhelmed, everyone adjusts to the transition differently. Don't second-guess yourself; YOU are your kids' Mother, and you're doing a WONDERFUL job no matter what gets or doesn't get done every day. Lack of sleep sucks, I know. Even when you're tired, try getting out for a walk around your block, or go to the park and just hang out. For one thing, it'll tire out your older kid as he works off pent-up energy, and your newborn will get fresh air that will make HIM sleep more, too. Just keep putting your newborn down while he's even half-asleep so that he learns to calmly go to sleep on his own. I always make sure that MY new baby is dry, has burped, and is drowsy enough for us to put her down.
The adjustment from 1-to-2 kids is STILL and adjustment for me, and I tell myself that at the end of the day, I'm exhausted, but ultimately, my kids are safe, healthy, and under MY roof with me.
I hope I was helpful, sorry if I came off judgmental or critical, just being honest. Before U know it, the baby will be 6 months old and will be going through OTHER ups/downs w/ growth/development. Just tell yourself that "this too shall pass" and just roll with it. What OTHER choice is there but to roll with it? You're doing a wonderful job just by loving them and being worried :)