Sounds like it is definently time to stop antibiotics and the prednisone and see what happens over the next 4-6 weeks. Prednisone can suppress your immune system. If antibiotics have not helped in a month then time to rethink the solution. Leukoplakia is a "pre-malignant" and progresses to squamous cell cancer in about 10% of cases. If you smoke, use smokeless tobacco products, alcohol (any form), or truly have irritation from teeth or dentures then focus on correcting these factors. It's a clincal diagnosis but biopsy should be performed. Oral leukoplakia on the buccal (inside cheeks) is usually benign but other locations absolutely need to be biopsied without watchful waiting. GERD (reflux) may cause sore throat or wheezing or early dental caries but my experience this is uncommon; especially in someone who doesn't feel this is a problem. Silent GERD during sleep is possible but hard to buy in your case. Migraines? You either have them or not so I don't buy that one either from your Neurologist. The only type of dentist to see is an "oral surgeon". These folks have the additional training to know something about diseases in the oral cavity.
Seeking a second opinion from a different ENT specialist unrelated to the first one is "smart".
You need a pat on the back for being concerned about your health.