An allergic reaction requires protein.
There is no protein in tobacco smoke.
What you are describing is hysteria.
It's not a food allergy, but it can produce headaches and sometimes sickness (as can chemicals in some perfumes, which aren't proteins either). I am not allergic to small amounts of smoke, but I do have a problem with some perfumes, and with smoke in large quantities (e.g., if I spend a few hours around a camp fire), so I know it can happen.