I've tried looking through many red dot sights, yet I still get the
same thing. Initially, I'll see one red dot, then in a few seconds,
the dot will grow until it splits apart, and I see a glob of a dot
with three distinct lobes.

I've tried this with both eyes open, one closed, switch eyes,
whatever, I see the same thing. When I try those sights that show a
ring, I'll see at least four distinct rings all forming an ellipse.

My vision is pretty good. What am I doing wrong?

The problem doesn't seem to be as bad with an EOTech.