It's normal for them to start asserting themselves at this age and earlier, and its fine for them to do that as they learn their boundarys etc. With teething, I know it can cause some pretty caustic teething poos to happen, but combined with the vomiting I would be looking at something else as being the cause. It doesn't sound like a gastro bug or other viral thing to me - maybe an intolerance or allergy? Besides the formula, has there been anything new introduced to his diet or anything?

I would be following his cues ATM with sleep and everything because he is so out of sorts that trying to make him follow any old habits will be hard when he is both unwell and going through some major developmental leaps as well.