I don't think there's any exact answer for this, mainly because every creature's immune system is their own- some work better than others at fighting off an illness or infection. Have you considered that this may NOT be an RI? By that I mean, have you checked in his nostrils since his last shed? BPs shed the outer lining of their nostrils along with the rest of their shed, but if they get stuck, those little bits of old shed can cause noisy breathing, popping or whistling- & so can water or other debris in their nostrils (or some combination). Pity they cannot blow their noses, eh?
What are the temps in the enclosure? Depending on how warm your BP already is being kept, sometimes raising the temps (cool end & warm end) by a few degrees can help them fight off an RI- but don't raise them to an unsafe level, obviously, because you don't want to fight an RI only to cause a heat injury or burn.
Do you have a local vet in mind that's well-qualified with herps? If not, this may help you locate one: https://arav.site-ym.com/search/custom.asp?id=3661