Lith formation in throat for months.

My daughter (10yrs) has been suffering from redness at the back of her throat and the formation of calcified lumps for several months - the production of these seems to be increasing. About 3 years ago she had the same thing and we were given antibiotics, which seemed to do the trick very quickly. This time however, we have been told it is viral and cannot be treated, so no antibiotics (even though they cured it last time!) - in fact we've now been to 3 doctors at our surgery and been told the same thing - six months on, and it's no better - in fact it seems to be worsening..
the lumps (Liths?) now come to "maturity" and fall out about twice a day minimum . Since we can't seem to get antibiotics, and it is only getting worse, can anyone suggest what we can do?
My daughter is otherwise healthy and of normal weight/height for her age, falling in the middle of the BMI range. She is physicaly active and lively (rides horses, climbs trees etc etc) . In the last month she has developed a dry cough - which manifests maybe 4-5 times an hour. She herself does not feel that it originates from irritation where the inflamation/calciferous material comes from. We are getting the cough seen to tomorrow, but since it is the same doctor who tells us the "virus" wiull go away (6 months ago) then obviously I'm not expecting any help from that quarter as regards the throat problem , so would apreciate any ideas short of flying to a country I can buy antibiotics in!!
Thanks.