If you have two white spots on your tonsils that don't cause you pain but are bothersome, it may be a white deposit called tonsil stones. These can sometimes lead to bad breath, discomfort, or a bad taste in your mouth. You can try rinsing your mouth with a saltwater solution or gently pressing on the tonsils with a cotton swab to remove the stones. Maintaining good oral hygiene by flossing and brushing regularly can help prevent further build-up. If the deposits persist after trying these measures for two weeks, it's advisable to consult a dentist or doctor for further evaluation.