I had four children, and I thought the transition from one to two was more challenging than from two to three or from three to four.
With two children (even when one isn't a newborn!), you need to plan your time differently. Everything takes longer! If you think you need five minutes to get all of you from your house into the car, schedule yourself ten or twelve. If you think breakfast should take fifteen minutes, plan on as much as thirty. If you think you need an hour to get children to bed after dinner, schedule yourself ninety minutes. You'd rather have planned too much time than not enough.
One thing this planning does is to help you think more calmly. Your big boy (who is still a little boy, although you don't mention his age) may be anxious about whether you love him as much now that he has a sibling - even though he may not be able to tell you so and even though he may not think of it that way himself. He certainly lives in a different kind of household now.
So make everything you can possibly manage into a "come help mommy" thing. Let him "help" you make supper. When it's time to nurse the baby, it's also time to read him a book. Let him help you with the baby by handing you a diaper or a wipe or a burp cloth when you need it (put the things where he can get them himself). Do as much talking to him and listening to him as you can, while you take care of the little one and the house. If your husband can drop him off at school even once in a while, then your son GETS to go with Daddy - special treat!
If the housework falls behind - and it will - ask you husband if he can help *temporarily* with little jobs until you get over this hump - or ask at your church or local high school about a good, reliable student who can come in for a while and play catch-up for you one afternoon every week for a little money.
Don't feel bad. Every mama has to learn these things. Sleep deprivation was always my worst enemy (it still is!). But do the best you can. Things will start to iron out. Your children don't need a perfect mama - just one who does her best.
And, one day pretty soon, take your big boy shopping and get him the coolest pair of socks he can pick out himself!