Lately I have had some dryness (like a skin rash) around the outside edge of my left eye, and in the winter I usually get dryness of my skin around the waist, and calves and ankles in my legs. I attibute that to low humidity levels in doors in the winter time. I have also had some grittiness in the eyes, but I do woodworking in my garage/shop and presumed it was coming from that. But I have not had any dry mouth that you mentioned.
FYI - My mother - who is now deceased - suffered from Sjogren's syndrome for the last 7-10 years of here life. It is an autoimmune disorder that causes dry eyes, dry mouth and some dryness in the lungs. To my knowledge the origin of that disorder is unknown and there is no cure....but the symptoms can be mitigated somewhat with eye drops and tablets for the dry mouth. Her condition also showed up with a red rash on the backs of her legs. She had a biopsy of her lip done that confirmed the condition. To my knowledge, it was never life threatening....but created some mild discomforts that she learned to live with.