It sounds like black mold to me. I have dealt with a lot of properties (im in real estate) that have it, and it can cause breathing problems.

Tea Tree Oil will kill mold, but really wont be of much use to you because you would have to soak the carpet and pad to kill it all. Your landlord should really take care of this for you. They sound like slum-lords to me too.

Here is a site about black mold: http://www.toxic-black-mold-info.com/index.htm

{{{{ Jan }}}} I hope the inspection goes well.