Question

Do non-metals also get corroded

Answer 1

Yes but we don't call it a corrosion.

Corrosion is a reaction of metal with water and or with oxygen. 

So,  when metal reacts,  they form oxides,  commonly referred as rust/corrosion when that piece of metal is a part of something.  Otherwise, it is oxides of iron, aluminum, copper etc..

In non metals,  oxides are not referred as rust or corrosion but simply oxides like carbon dioxide, nitrogen oxide,  phosphorus oxides, etc etc..

Answer 2

Yes non-metals also get corroded.