Sounds like Tonsil Stones. The little White things are probably Tonsil stones and they do stink like hell! Many believe that Tonsil stones is from your tonsils filtering out toxins and other bad crap in your body.
Not much research has been done about this (That I know of) and it blows my mind. There is ways to take care of it. One thing I would do every day is take something and push into your tonils and get those stones out. Thats what I did. The next thing I would do is start oil pulling. There is plenty of info on that.
Then start juicing and pumping high quality nutrition into your body. See what happens. Heck even look into H202 therapy. Detox your body man. And make sure to exercise and work up a good sweat on a regular basis.