What's a good remedy for dryness in eyes or tear glands?

Lots of options: There is no one best option. What you want to use is an artificial tear drop or, if the condition is more severe, gel. The types with "get the red out" medicine i advise against. In mild dry eye, i usually recommend a 3 times a day schedule, regardless of symptoms. If that isn't sufficient, you can increase it. Persistent symptoms despite frequent use should prompt a visit to an ophthalmologist.