Hello,
I have dealt with this exact issue for the past 8 or so years - a painful “thump” in my right ear when sound is presented to left ear while right ear is covered. Like you stated, when both ears remain uncovered it is rare to experience this thump, but it will occasionally occur with certain frequencies. The “thump” is unique, not a “flutter”, and differs from any sort of tinnitus I’ve experienced. The onset was random; one night I just noticed it happen as I was watching TV. As the years have progressed, this thump has become more painful and easily triggered to the point where I have had to change certain behaviors (for example, positions I sleep in as even the smallest sounds from other areas of the house now trigger this “thump”).

I am currently seeing an ENT for this. My hearing test and audiogram are within normal ranges. We have ruled out MEM (abnormal middle ear muscle movement of tensor tympani and/or stapedius) as no middle ear muscle movement was detected when recreating the “thump” with an audiologist. My brain MRI was normal and showed no evidence of any sort of mass lesion or other abnormality. Our next step is a brain CT to look at the temporal bone to rule out SSCD. My ENT has consulted with numerous other ENTs and surgeons and no one can come to a general consensus on what the issue might be. If a clear diagnosis is able to be made upon further testing I’ll reply with an update. I hope this helps.