You're quite right - 19 yr old doves are extraordinarily long lived. In fact, according to Stanford U. the longest recorded life of a mourning dove is 19 years, 3 months.
In any event, the symptoms you've described could be anything from a respiratory infection (yes it would cause the eye symptoms you see) or some other infection in the system.
Since there's no way to know without hands on testing, the only thing you can do is palliative (supportive) care and I'll help you with that.
Now remember, this bird is very likely at the end of his lifespan anyway. The choice to be made may not be so much getting him treated, but making the decision to help him go painlessly with a vet's help, or just trying to make him comfortable at home and waiting it out. With this choice you may be prolonging the poor bird's pain and suffering though.
You'll want to make a 'brooder box' which is an 'at home' hospital room:
use a small box lined with soft clothes like tee shirts.
Use a thick, clean sock and fill it ¾ with plain, raw white rice. Knot the end and microwave it for about 1 ½ minutes. Shake it afterwards to distribute the heat and be sure it's not too hot. Tuck this in just under the cloths.
A heating pad under the box is also helpful, set on low. This is one of the few times I’d ever use both heat sources if necessary to maintain incubation temp (90-105 degrees).
If ever using an electric source for heating anything in anyway, please be vigilant and constantly double checking carefully.
Gently drape a light cover over this box to further help hold heat in and keep light low.
Treat his eye with a gentle, warm water wash. You can use the sterile solutions in any drug store that's typical for contact lens cleaning.
Soak a cotton ball in the warm water or the sterile wash and gently dab at the eye rather than rub
Make sure food and water are available. Dissolve about a teaspoon of plain, real sugar in about 1/2 cup of water and let the bird drink this. Baby food rice cereal (in the baby food aisle) might interest the bird in eating.
Once the bird stops eating and drinking you have to really consider that it's in pain and it may be time to see the vet
I'm so sorry that you're going through this. My heart goes out to you