To answer your first question, dehydrated skin usually does not have a "puffy" appearance to it. In fact, classically in medical school students are taught that looking at skin "turgor" is a good way to gauge someone's relative hydration. Meaning that if you pinch an area of skin on a person with dehydration, the skin tends to stay "bunched up" for longer before smoothing out when compared to the same person when well hydrated. Inflammation on the other hand can definitely cause your skin to become tight, and give a swollen appearance. The question then become why is there an inflammatory process going on in the skin of your face. You are correct in questioning whether this may be an allergic process, as that could be one of the possibilities, however there are multiple different possibilities as to what might be going on. I would recommend that you make an appointment to be evaluated by a dermatologist
, as they will be able to determine what process might be causing your skin to be tight and "puffy" and also help determine the underlying cause. I would recommend making a list of recent products used on your face, during routine bathing, any recent medication changes, and bring your medical records so that they have all the information that they might need. Best of luck.