In my experience, the sound level alone at the gym would mean the gym is a no-go. The exercise may be putting stress on your system. Usually, people complain about PCS head aches that are triggered by exercise. Apparently, you are not struggling with head aches.

Learning to ignore or not pay attention to the ringing is an important skill. My ears ring 24/7. I have learned to just ignore it. Getting frustrated often makes the ringing louder.