Is this possible?
Perhaps. A quick review of the literature reveals two to three case reports of normal saline allergy. One was published recently in the American Journal of Emergency Medicine this year which reports on a woman who became tachycardic and developed a erythematous rash after administration of sterile NS.
I'm a bit incredulous but I guess anything is possible. Despite Darwinian forces which generally eliminate people with significant allergies to the basic elements of life, perhaps some still sneak through. Anyone ever hear of an oxygen allergy?
Source
Ay, D. et al. "An unusual cause of allergy: case report of normal saline allergy" American Journal of Emergency Medicine. v 27. 2009.