So after getting some new fish that I thought were healthy it turns out that they have ich. I already put them in my main tank so I'm not sure what to do at this point. My tank is cycled and if I clean it out that will kill all the good bacteria, won't it? I mean, I can't keep the filter media if the ich has infested the whole tank can I?

No you don't need to take anything out of the tank or clean it at all. Ich is normally treated with heat and salt. You don't mention what fish you have in your tank - just make sure your species can handle the salt and warmer temperatures!