Your best bet would be to go back to the hairdresser and ask them to fix it. You've already damaged those parts of your hair enough (as it sounds like it's been over processed) so you don't really want to be putting more damaging products I.e box dye on your hair for risk of further damage. But if you do want to put a box dye over it, wait a few days at the very least and condition well. Without knowing what colour you choose, I can't tell you how it would turn out but darker colours should be fine (semi-permanent or less, to reduce damage).