BLUE TONGUE SKINKS

My 7 month Indonesian bts was diagnosed with respiratory issues 3 weeks ago, with the symptoms sneezing, deep breathing, open mouthed breathing and wheezing and whistling when breathing. He was put on a ingestible antibiotic first two weeks when he went back for his checkup due to his continued sneezing he was put on them for another two weeks. His other symptoms seem to have gotten better but I saw him with his tongue just sticky his mouth and he started to make a wet clicking noise When he breathes but only sometimes I don’t know if he still breaths with his mouth open as I’m not with him all the time but I’ve not noticed, me and the vet both saw an improvement in his breathing but his 2nd batch of medication is finished in a few days and he’s still sneezing, has anybody had something similar, does anybody know how long it takes them to get over it I’ve read from weeks to months, should I trust the vet? Could it be viral? Is there anything I could do to help more? Should I be worried? Any help would be appreciated