Coughing up White specs for almost three weeks.....please HELP.?

I am not a doctor and this is simply a hunch but it could be a bacteria filled substance in your tonsils. I have had that many times. It is a white spec/soft stone type of material that simply builds in your tonsils... As far as I know, it is harmless, but if you look at your tonsils and see "white stuff", take your finger or a cotton swab and try to pick it out. It should come out easily. No need to tear or pull, it simply lays on the surface and is not attached to the tonsil. I would listen to your doctor, and know that what you have may not be what I am thinking... But also make sure that you are NOT hurting yourself to get white stuff out if it is there!! If it is what I'm thinking, it will not be attached, just sitting there. Hope I helped! Get better soon!! :)