Hello & Welcome to Just Answer,
Having gone through your description, I think that we might be dealing with the problem of “tonsillolith”. Please have a look at this pic:
http://oridoc.co.kr/zeroboard/bbs/icon/member_image_box/1/tonsillolith.jpg
You will find some helpful hints at this web resource:
http://en.wikipedia.org/wiki/Tonsillolith
there could be a few issues which might need attention:
(a) Malnutrition
(b) Food allergy
(c) Stress
(d) Thyroid hormone imbalance
However it would be best if you could check in with your doctor for this, and I am sure that your doctor would also be having a look at your chest problem and would be managing it appropriately.
I hope that it helps. Best wishes. Please feel free to enquire if you have any remaining concerns or doubts and it would be my privilege to try helping you as much as I can.
Doctor
Veteran; amongst 'Top 100 Scientists', 'Top 100 Health Professionals', & Who's Who of the W