It could be a fermentation problem. If you fermented too warm, especially if you under-pitched or under-aerated, you can get some plasticy, solvent-like, and/or medicinal flavours. Rarely do you get plastic flavours originating from your brewing equipment, unless you use something that wasn't designed for that purpose.
Without tasting the beer, it would be hard to say what the cause could be.
Oxidation effects do NOT taste like plastic, though. They contribute a stale, sometimes cardboard-like off flavour to beer.