My 4 y/o daughter has several white spots on the right side of her throat, she has no pain or swelling, mild drainage and a cough.

ulcers in mouth: it sounds like your daughter has a virus that is causing the ulcers the back of her mouth or throat. These ulcers with cough and postnasal drip are caused by virus. Tylenol (acetaminophen) or Motrin by mouth if she develops fever or pain in her throat. Coolmist vaporizer overnight will help. Decongestant by mouth will help. If not improving, drinking less, or peeing less, take her to Dr.'s office

Hard to say: without looking at them. Tonsil stones are a possibility . May try using warm salt gargle or mouth wash rinse. May need referral to ENT if concerned or having bad breath issues!