How possible is it to be allergic to cotton? what are symptoms if so?

Possible.: One may be allergic to just about anything. Symptoms would be the same as with any other allergy - skin rash on exposed areas. If the cotton fibers were aerosolized one could have itchy, watery, red eyes and watery, sneezing nose.

Possible but: I have never seen one nor have read any published data on it. If you are indeed allergic to cotton (skin rash from contact) , the allergen is more likely coming from chemicals used to treat the cotton than the cotton itself. I said possible because one can never say never in medicine.