Hello,
These deposits are not unusual and commonly known as tonsil stones. They can have a foul odor. Try to rinse, avoid irritants and keep well hydrated. If large or you are unable to remove, you can visit your ear, nose and throat specialist for removal assistance. You will then have the opportunity to have your throat fully evaluated for a thorough diagnosis.
Treat your throat with reduced exposure to irritants. Avoid alcohol and smoking. Stick to a bland diet. Evaluate your climate control unit. Dry heat may require a humidifier. Any sinus complications that affect breathing or produce a post nasal drip? This can be harsh on your throat. Dental problems need to be addressed and make sure that you are up to date on your dental exam. Infections, periodontal disease, grinding or a fungal infection could produce some of your symptoms.
Are you on medications that have side effects such as producing a dry mouth? Try dental products such as rinses, gum and toothpaste designed to help increase moisture in your mouth.
I hope my suggestions are helpful and thank you for your inquiry.