desiccated is a good word for something being harshly dry, but it is not specific to eyes, so you would still have to write "desiccated eyes."
Bleary is a word specific to eyes that are unfocused, possibly by fatigue, but not necessarily by being dry.
of the eyes or vision : dull or dimmed especially from fatigue or sleep
The word blear can be a noun, but it likewise doesn't imply dryness.
a film over the eyes; a blur.
You could combine the words if you want to emphasize the condition with colorful language:
His vision was obscured by a dessicated blear.
If you're going to take this approach to describing the person's state, you have a lot of options. A thesaurus would give plenty of variations.