Welcome in H.C.M.
I have gone through your query regarding recurrent sores on nostrils and at present our both nose get involved and tender, even after taking Bactrim
As per your clinical history it appears as you are most probably having recurrent vestibulitis of nose. Here i would like to suggest you these basic investigations-
1- Blood sugar (F & PP)
2- Culture and sensitivity of nasal smear.
Beside this local examination of nose by an ENT doctor is necessary to rule out any local pathology of nose leading to recurrent infection.
In this way one may get the facts behind your disease and that may be accordingly manage.