Dry eye is the most common eye condition in today's era.
I think you're mistaking blood vessels in the white part of the eye (called scleral/conjunctival blood vessels, visible from outside) with retinal blood vessels (inside the eye, not visible from outside)
While dry eyes has no direct correlation with retinal blood vessels, dry eyes can cause redness in the outer part of the eye, by increase irritation of conjunctival blood vessels.
Next Steps
Use lubricating and moisturising eye drops
Hydrate well
Health Tips
Wash eyes with cold drinking water regularly