Dentist placed a veneer 3 days ago, my mouth is constantly burning and is drying my eyes too. Is this normal?

You are possibly
experiencing a side-effect from a material used during the preparation at your
appointment. Do you have a latex allergy? Perhaps you had some gum irritation
from the acid etc, cement or topical anesthetic. If your symptoms persist more
than a week, see your dentist for a follow up. Most tissue irritation will resolve
itself within 7-14 days.

Mouth burning and dry eyes after a veneer being placed are not typical post-op complications related to treatment. Possible explanation for feeling of mouth soreness or burning could be related to irritation caused by the etch used in bonding the veneers. The dry eyes most likely is unrelated, but in theory a low percentage of patients are hyper-sensitive to the epinephrine in the local anesthetic. I suspect your symptoms should improve within a week or so.