Its pretty normal to dream... I really doubt there's anything you can do to not dream. But, maybe you can practice lucid dreaming and talk to your subconscious and tell it to quit with this tinnitus shit.
Can anyone here do lucid dreaming?
I came really close once a couple years ago. I remembered reading somewhere to try to remember to look at a clock, or text in a dream, look away and look at it again, and if the text or time is different or blurry that surely its a dream. I did that once, and had a 'oh my god!' moment in my dream, realising I've just become aware that I'm dreaming, and consequently woke up lol.