> I'm right eye dominant, though, so I throw, swing, shoot, use scissors, play instruments and use a mouse right handed.

Dominant eye and hand don't have to match; in fact, they often don't. To quote Wikipedia:

> ...the side of the dominant eye and the dominant hand do not always match. This is because both hemispheres control both eyes, but each one takes charge of a different half of the field of vision, and therefore a different half of both retinas