Is 16 units of botox too much for the eyes area for someone with no wrinkles?

It does sound like you may have received too much since it's caused complications, or the injection technique was not accurate. I suggest you follow up with your injector.

Perhaps you had too much injected under the eye which is affecting the constrictor muscles and not allowing you to close your eyes fully and because of that dry eyes. Consult the injecting physician or an ophthalmologist for guidance. Dry eyes can cause a lot of problems, especially if it is iatrogenic. 

The average number of Botox units for the crow's feet is between 5-15 units PER SIDE. So you fall right into the middle there. While you had what would be considered a normal number of units, injection technique is key and that's probably more of the issue. "This answer has been solicited without seeing this patient and
cannot be held as true medical advice, but only opinion. Seek in-person
treatment with a trained medical professional for appropriate care."