If you're someone who's tried triptans, NSAIDs, Botox, CGRP drugs, supplements, essential oils, elimination diets — and is still suffering — cold therapy works on a completely different mechanism than any of those.
Pills work on chemistry. They have to be absorbed, metabolized, and reach your bloodstream before they touch the pain. By then, the migraine has already escalated.
NeuroSoothe works on physics. It physically constricts the dilated blood vessels pressing on your trigeminal nerve, and the cold sensation interrupts the pain signal at the source. There's nothing for your body to "process." It works the moment it touches your skin — which is why it works on attacks that pills don't.