Do you mean you're allergic to some common additive in table salt, or specifically to elevated salt concentrations? The former sounds like something you could call an allergy (but not to salt itself); the latter I probably wouldn't call an allergy so much as higher sensitivity to significantly hypotonic food or drinks. An allergy is usually defined as an excessive, damaging immune reaction to a foreign substance that is itself harmless at that concentration. Salt isn't a foreign substance.

I get the feeling a lot of people are lumping tons of things into the category of "allergies" where the underlying biological processes are very different. That doesn't mean the reactions aren't real, but it makes it very difficult to reason to reason about them. When everything's an allergy, the word allergy stops having any useful meaning.