katchoo_too's recommendation for an ophthalmologist turned out to be really good. She was very careful and thorough, and diagnosed something 25 years of doctor's visits had missed: that my eyes don't track together at a distance of more than a few inches. My brain has learned to compensate except when I'm tired or been staring at a screen for too long, but if they had diagnosed it when I was 10 they could have done something about it; now the brain has gotten so adjusted to doing the processing that it can't be fixed.
I had recognized the problem, but had thought it happened to everyone. Apparently not. I should get an eyepatch for those times that I lose tracking, since trying to keep one eye closed when driving or at the computer is annoying.