fur feeling/sensation on back of tongue

Hello,
I am 46 year old female and have noticed in the last 2 months a feeling of a hairball on the back of my tongue/throat.
I had rai therapy for graves in June of this year. I have been on Levothyroxine 100mcg a day for a few months now ( I was wondering if this feeling is a side effect of the drug)
I have seen my dentist and doctor for this problem to no avail. The Doctor said I had swollen nodes on the back of the tongue and said use zinc tabs and I took z pak to no avail and then took amoxycillian and that did not help. The dentist said I had swollen lingual tonsils and I had my tonsils out when I was twelve. I always have a lot of phlegm in my throat and always find my self clearing it. What else could I try? I called my Doctor again today and he said take more zinc, it is not helping and I told him he said well you will have to see an ent. Please advise, these visits cost money and they are becoming frequent with no relief.