Welcome in H.C.M.
I have gone through your query regarding your sore throat
and coating of tongue. As you said durng cleaning of mouth you find peeing of white debris from back of your tongue and you are worried about.
As you said you are already taking medicine from your military clinic. Your doctor had given you medicine without taking culture is doctor's own decision which depends on clinical findings, If your fever
etc have gone soreness is also diminished than don't worry and continue treatment.
Peeling of white slough after gargling during mouth cleaning is good sine of recovery.
Hope your query is clarified.