ENT prescribed me fluoxetine

I went to an ENT for the first time today. I have extreme clicking in my ears. It’s so loud someone across the room can hear them. Everytime I swallow, talk, move my head, etc my ears click. She said I have patulous Eustachian tubes, and offered me two solutions.

The first solution being an injection near my ears click tube to “close” the tube. Which she did not act like she wanted to do/it being risky.

The second solution being she prescribed me Fluoxetine. She said it will help me not care as much about noises…

This is the first time I am researching this, as I finally have a name on what’s going on. Is there any suggestions someone can offer me, and possibly where to start looking for treatment?