This may be a impossibility but here goes, is it possible to be allergic to cold temperatures? If it’s possible then it’s UBER rare granted, but still it might be possible non the less. If it helps I read about it in a book once , I forgot which one though.
There is no true allergy to cold, but there is a condition called cold urticaria, which is a subtype of physical urtiaria. Other subtypes of physical urticaria include increased sensitivity to physical pressure, water, heat, sun exposure, etc.
Cold urticaria is a skin reaction to cold that appears within minutes after cold exposure. Affected skin develops reddish, itchy welts (hives).
The condition most commonly occurs in young adults.
Allergy, which is an exaggerated immune sensitivity to certain environmental compounds, usually plants, or less commonly microorganisms, metals and other materials.
McConnell, Thomas H. (2007). The Nature of Disease: Pathology for the Health Professions. Baltimore, Mar.: Lippincott Williams & Wilkins. p. 159. ISBN 978-0-7817-5317-3. Archived from the original on 8 September 2017.
Cold temperature is not an environmental compound and thus can't trigger an allergy.