Is he napping well? My son turns into a total monster when he doesn't get two solid naps a day. And he should be sleeping 11-12 hours a night, as well! Maybe give him an earlier bedtime?
If that stuff is all good, and he's also doing fine with food and milk/formula, then I recommend that you get an Ergo carrier. They are much easier with big, heavy boys like ours. You can put him on your front or back, and it doesn't hurt your lower back or shoulders, like other carriers do at this age. I would just wear him a lot- both around the house and out and about. He's probably going through a clingy, scary new phase because of all his new skills. This is an exciting, difficult time for babies! Being close to mom can make all the difference.
Also, Dr. Sears says that good attachment often leads to a very difficult, but short, period of intense separation anxiety. It actually means you've done a REALLY GOOD job at seeing to your son's needs, and he's now developing the necessary anxiety and hesitation he needs to one day make good choices about his safety!
It's a rough time, I know. But keep staying positive with him, keep taking him to those classes, and keep doing your normal routine with him. Nobody should give you a hard time about your son's outbursts. Give me a break- he's only 9 months old! He's figuring it out, just like everyone else! Try hard to ignore the rude looks. I have to do the same thing with my 10 month old, who tantrums badly at times. As if their kids are perfect??
Boys are hard. My son's strong frustration reminds me of my husband sometimes! :)