I was suggesting henna as it is a gentle course of action but any medium brown will do. You will only further damage the remaining healthy hair by lightening it as darker colors do not "thin" and strip out proteins. The darker color will not further damage the root structure of the hair so your hair will be allowed to bounce back more quickly.
The hair that is damaged is damaged. However, we are attempting to make it look reasonable for interview. The darker hair color should "weigh" down the damage hair and the olive oil on the tips should give it a natural healthy sheen.
My thought, as much as it pains me to say it, is after the interview you're going to need to cut away damaged hair and allow it some time to grow out. You will be able to have your hair "fake it" through the interview but if you really want to get back to having healthy hair that bad stuff's gotta go. Think of your hair as you would a plant. If you trim away damaged leaves and branches it grows quicker. The same is true for your hair.
A fun idea for when you want to wear color in your hair is go and get one of those "hair extension" clips at your local store and decorate that. I keep several. I have a few that are colored, braided, and beaded. It allows me to be creative and dress up my hair without damaging it.
You are going to look fabulous and shine at your interview!