At the end of Stranger Things season 1, we can see Will puking up a slug in the bathroom. A year later, the events of the second season occur. In the second season, we can see D'art grow to become a demodog in weeks. That means the slug that Will vomited had more than enough time to become a fully grown demogorgon. But there weren't any fully grown demogorgons in the second season.
There are too many unknowns to answer that but there are a few possibilities. But first, we have to guess - are demogorgons and demodogs the same specie? It is quite probable that demodog is just an immature stage of the demogorgon (and the Stranger Things Wiki seems to confirm this) - those two look quite similar, you could even say that demogorgon is bigger and bipedal demodog. There are many species that have such complicated life cycles with different stages looking very different to previous ones - for example Phylloxera has 18!
If we'd assume that they are, then it is quite possible that D'art WAS the same slug that Will puked - it has stayed hidden slowly feeding (or even more possible - in hibernation waiting for signal) until it was big enough to process to the next stage.
If we assume that demodogs and demogorgons are not related, then either the slug that Will puked died, it is still hiding somewhere or it was just a demodog, not demogorgon slug.