It's a nice little Phalaenopsis, Aimee. I'd be sure to rinse off the soap you used on the mites with a spray of warm water.
Also it's extremely important that the pot your orchid is in has drainage, and air holes. Looks like it's in a little tin bucket that maybe doesn't drain. Those type of orchid like to let their roots dry out between waterings, and they like their roots to have lots of air in general. Check that there isn't a huge wad of soggy moss in the pot, which is very common for BBS orchids. That will spell certain death by root rot.
It will need some light to survive, too. As long as you can keep it 5ft. or so away from the other plants it might be better to bring it nearer to a window.
