Valene, I hate to add a suggestion from left field, but it seems unusual to me to have one eye worse than the other. I *do* have that, where my right eye dried out so much that it affected the cornea -- a condition called corneal opacity. The old cause was a third cranial nerve injury from an ancient traumatic brain injury. That tended to dry out my right eye. Then, when I got the temporary condition known as Bell's Palsy (autoimmune, inflammatory, swelling disease of the 7th cranial nerve), first tears ran down my cheeks especially from my right eye, and then the right eye dried up.
You might ask your ophthalmologist that you see on Wednesday whether s/he would consider a referral to a neuro ophthalmologist, who would look not just at the eye itself, but at the nerves that control the functioning of the eye.
I can think of at least a half a dozen responses your doctor might have, so it may not be the easiest conversation. And I could be wrong, too. I'm just saying that injuries/swelling in the cranial nerves can affect a single eye, and one of the effects can be excessive dryness.
Good luck,
Soycoffee