Sorry, but 55 tot 65 grams is a huge difference (10 grams out of 50 or 60) so a very unclear measurement to work with.
You need a better vet!
Any vet (even an ordinairy dog&cat one) should be able to discern between mites and some kind of nasal reaction.
->
Mites can be found bij scraping the surface/ even inside the 'nostrils' of a bird, they are tiny animals so they show up under a microscope.
Rhinitis is a condition induced bij either a virus, bacteria, allergies and/or particles... so treating this with antibiotics is gambling in the dark!
Antibiotics only help when there is a bacterie there, it does not do anything against any virus, dust, allergens etc.etc. and even so you need the right type of antibiotics with a certain type of bacteria -> they are not a fix-all. So your vet needs to do a culture / grow that stuf in a petri-dish and decide if and what type of bateria are present and then use the right antibiotics.
It is not rocket-science, just common sense with a little bit of Sherlock Holmes
Try and get hold of some birdy-probiotics.
Antibiotics kill of usefull gutbacteria as well --- and those the bird needs for his digestion as well as the imunesystem!
So always feed your bird probiotics when he is on anti-biotics and some time after that as well.
(Some people give the bird probiotics all the time, that is fine too.)
Just make sure the space where your bird lives is as dustfree as you can make it (in case of allergic reaction) and try to find a CAV.