Had a reaction to hair dye, itching, swelling. What can I get over the counter?

There is nothing you can get over the counter for what you describe. It sounds more like you have a burn.

Had a reaction to hair dye, itching, swelling. What can I get over the counter?

You need to get in. When you have that especially from hair dye not only can the doctor help he can tell you what in the hair dye you are alliergic to.