I have observed among my friends that having a second baby is often a lot different from the first baby. How old is your firstborn? If you have a toddler or small child running around plus an infant, that's really tiring. Also the lack of sleep is going to throw your moods out of whack. I hope it helps a little to know that what you're going through is not unusual. It takes time to make this adjustment and that is OK.
See if you can arrange with someone to babysit the children every so often, or at least the older one, to give yourself a break - maybe an aunt or another mom, or grandma? Even just an hour so you can take a nap might help.
You may also be suffering from postpartum depression, which is TEMPORARY and TREATABLE. It is not a character flaw and does not mean you are a bad mother. Ask your doctor about it, either whoever you see for the well-baby checkups or your OB/GYN.
Once your baby can sleep through the night, and you can too, then I bet things will feel a lot better. You can get through this!