Hi S.,
First, I love hearing that you're a Special Education teacher. At 32 years old, I am currently going back to school to do the same myself. I'm very excited!
Second, your son’s behavior is completely normal, especially with a new little one in the house. It should really be called the "terrible" 3's instead of the terrible 2's. My older son (now 4½) changed from a super sweet and quiet kid to quite the monster when his little brother came into the picture (from jealousy and feeling slightly abandoned - even though he wasn't, that's just how it felt to him). Plus he turned 3 a few months afterwards. The first year was particularly hard, since I really had to spend A LOT of time and energy trying to remain calm, while staying firm and consistent (the key ingredients) with my older son with time-outs and talking about how to handle situations (which part of what they're learning to figure out, so it's good to give them a game plan for common conflict situations), while also trying to give him positive attention and take care of my infant son. Things are starting to get better now that they're starting to play together more, but it was certainly rough for awhile. (At least for me.)
Also, I suggest trying to use a rewards chart to change things into positive reinforcements rather than just getting punished when doing something wrong. That's helped us a lot. Ours includes things like sharing toys, no harming or yelling, cleaning up mess and good behavior in public. We also used it for potty training when we were in that stage, which helped as well.
I hope this information at least puts your mind at ease that it's not just your son. He will work through it, but he will need a lot of help and it WILL be very frustrating at times. (Especially if he starts physically acting out at your younger one, which is VERY hard to deal with calmly.) Just keep your head up and do what you can. And make sure you get SOME time to yourself to unwind every day. :o)
Good luck!! :o)