Would you believe that there is such a thing in pets as an allergy to plastic? No joke. And in my experience it's one of the more common ones. I'll see several suspect cases per year, and they generally appear very similar. The pet will come in with irritation or a rash around its mouth. It's usually a noticable problem but not a serious one, so it can be overlooked or ignored for a while. In severe cases there can be some localized infection and discomfort, though it is almost always limited to the area around the mouth and chin (basically, anywhere the pet can closely contact the bowl).
Thankfully, this is very easy to rectify. No need for expensive testing, chronic medications, or visits to specialists. Switch to ceramic or metal bowls and the problem is diagnosed. If it goes away in a week or two, it was an allergy to the plastic. If not, then further investigation is needed. And if it's a plastic allergy you can cure the problem by simply avoiding plastic bowls. However, I would still recommend having your vet examine your pet and not trying to self-diagnose.
See, not every medical problem is complicated or expensive!