Does hair dying damage hair

A good general rule is that the lighter you go the more damage you'll get. The drugstore brands are bad for your hair because they don't work with the natural structure. I get people who come in at least three times a week sobbing because their hair is orange/red/MUD and NOW they decide that they want a professional to fix it. Had they come to get their hair colored at a salon first it'd have been less expensive all together.

Now there are professional colors that actually improve the state of your hair.

Like I said, not knowing you or your hair, I think your best bet is to talk to a real stylist. Consultations are almost always free and a good colorist will take the time to help you and be happy about it.