Can you have an allergic reaction to hair dye even after you have washed it multiple times?

See about 2 weeks ago i dyed my hair and a few days ago my head started getting really itchy and irritated. It hasnt gone away so i read the ingredients on the dye and it has an ingredient in it that im allergic to but my mom said that it shouldnt be from the hair dye because i have washed it and its no longer on my scalp but im not using anything else that im allergic to and its only on my head. So im wondering if it is the hair dye or if its probably something else. Experienced answers please! Thanks! :)