Hi HB,
Dry eye syndrome sometime manifests in excess tears, ie opposite to dryness. You should discuss with you GP. Excess tears are frequent in the morning hours as you describe. Low estrogen is one of the causes of dry eyes. Artificial tears help alleviate the symptoms, also high doses of Omega 3 s. ive had dry eye syndrome for 3 years now and I think Hrt has helped a lot!
Good luck!