It is possible to be allergic to the dyes used in hair highlights. It could appear in a lot of different ways, such as a rash, redness or irritation. Breathing difficulties are another possibility. You could have irritated eyes or lungs from these chemicals, if you are allergic, as well. Hives are another possibility.
Do your roots hurt? Are your rooting changing to an abnormal color? Is there itching or pain? You can be allergic to anything even if you were not adverse to it in the past.