I am not a chemist or scientist, but I did work as a hairdresser for many many years, and I never heard of anyone having a skin breakout last that long from only a few applications of color. If anything someone might experience an allergic reaction right away. Otherwise, I think we just soak up the toxins and they may cause Acne on the way out while being detoxed.
Bromide is in so many things, I believe just a few hair colorings isn't going to be the cause of your acne.