Hi Grace and welcome to Orchid Board
If you have rotting roots then you need to repot. Remove all the medium and wash it off the roots, then remove all rotten roots (they are rotten/dead if they are squishy, gently try squeezing them, if they are firm they are still alive).
If you have lots left then you need to pot back up in fresh medium. Now medium can be difficult, a lot of the stuff sold in shops is not the best quality.
I think the best thing to do is to try and get a picture of what is left of the roots and post it here. We will then be able to advise what to do next.
You may find you loose the flowers trying to save the orchid, if keeping the plant alive is important to you then that may just have to be one of those things.