As a Dark Elf, I went and became a vampire but the glowing eyes just turned me off from playing as a vampire. Is there a way to not have glowing eyes as a dunmer vampire. I really would have to hate relying on just the Nord since the eyes look ok and aren't glowing.

Uninstall Dawnguard, or mods are your only options.

On consoles, no way. But if you're on PC, you might just be lucky.