It is not plagiarizing if you are copying your own work, unless your original paper was plagiarizer. I would re write the paper but you could use most of what you did two years ago. Hopefully you are a better writer so you should be able to make some improvements.

If its your work its not plagiarizing. As for the teacher finding out idk. Are the colleges in different states? If so probably not. Is the class big? If so I doubt the teacher is going to check every students previous papers to see if they were used before.

Reusing your own work isn't technically plagerization. It's academic dishonesty. If your professor runs stuff through software like Turn It In, it'll show up, and you'll fail.

However, in circumstances like this, you are allowed to ask your professor if you can reuse your old paper. If he says no, then you cannot do this. However, you can also ask him if you can use it as a reference for his paper - and then rework it for his class, actually citing your old paper as an "unpublished paper" in your reference page. In this way, you can benefit from the work you already did, yet rework the paper so it fits in with what this new professor wants, and is also better than your old paper - all completely above board.