White spots in the back of your throat could be due to many things. Usually, any changes in the inside of your mouth or throat away from the normal, pink mucosa is a sign that the body is responding to some sort of chronic irritation. In your specific case, as you already know that you have bad allergies, it is quite possible that your post nasal drip is a constant irritant to the back of your throat that is causing the body to respond by producing extra phlegm/mucus to protect the surface of the mucosa. You should be able to reduce the post nasal drip either with nasal saline rinses or with the addition of an intra-nasal steroid spray such as Flonase or Nasonex. Either of these help to decrease the local inflammation and mucous production, which should stop the flow onto the back of your throat. Obviously, getting away from the mold is also important. (If your allergy really is to the mold, however, it would be expected that your allergies would be year round. Fall allergies (and other seasonal allergies) are usually due to seasonal things such as ragweed. Please speak with your doctor
to determine if your white spots are due to allergies or something else that you need to treat.