2 years ago I washed my eyelids with dish detergent once. Clearly a very dumb idea, and my eyestrain has definitely been worsened by this, since then. My eyes are now sensitive to any kind of tiny foreign material inside them - be it a dust speck, or e.g. some minor sweat-grease from accidentally touching my eyes with my unwashed fingers.
The good news, though, is that rinsing my eyes with saline solution (from the pharmacy) before using a screen, helps me a lot. A lot more than even the best "artificial tears" available. Artificial tears (i.e. moisturizing eye drops) seem to "lock the irritant in" into my eye, and hence just increase the eye irritation (usually).
Try it! On the off-chance that you have a similar eyestrain etiology like mine, it might help you. 🙂