Is it possible to be allergic to neosporin?

Possibly. It is possible to have a true allergy to neosporin or one of the ingredients of neosporin. Additionally, neomycin (one of the ingredients of neosporin) can be irritating to the skin, especially if used over a long period of time or if covered by a bandage. Although this reaction is not a true allergy, the irritation often has similar characteristics of an allergy reaction. See your doctor.
Yes. Neomycin, the antibiotic in neosporin, is a frequent skin sensitizer leading to allergic skin reactions.