**I am not a doctor, nor any other type of medical professional. This is based on my own research, allergic reactions, etc.**
If a person has a PG allergy, they'll likely react to many, many personal care products (hand sanitizer, deodorant, etc.), and possibly some medications with PG. Symptoms vary, but some that one might experience with
vaping PG are rashes and/or hives, scratchy
throat, headaches, nausea, and shortness of breath. I've heard of people not reacting to contact on skin, but still reacting to inhaling PG, but I have no idea how common that is. The symptoms may be brief or last several days after an allergic reaction.
And yes, someone can be allergic to VG. Allergies to PG are rare, but I'm not sure about VG. I've heard of fewer reports of VG allergies than PG, though my experience is limited.
With PG sensitivity, you may experience similar symptoms to an allergic reaction (I'm PG sensitive, and have to be careful about products I use, including
e-liquids), but not as severe. A higher VG content will usually alleviate the problems. I imagine the same is true for VG sensitivity.
If you suspect a PG or VG allergy, I would highly recommend seeing a doctor to find out for sure.