Is it possible for allergies to make your skin itchy but not look different than usual?

Yes but...: In most cases of itching caused by an allergy, some kind of rash (like hives) will be apparent. While allergies could cause itch only, other things should be ruled out such as problems with the kidneys, liver, gallbladder, & thyroid. In addition, infections (hepatitis, hiv, parasites), diabetes, iron deficiency, and malignancy can present with itch as well. Consult with an allergist to make sure.

Yes: Allergies can indeed be causes, but often the reason for itching can be elusive.