To the best of our knowledge, prolonged computer use does not damage the health of the eyes, but can cause some very annoying symptoms. Try taking frequent breaks, perhaps every 20-30 minutes: close your eyes for a bit, go get a sip of water, look away from the screen. Decreasing the glare on the screen may certainly help. Lowering the computer monitor will bring the upper lid down a little, so your eyes are not as wide open, and thus there is less evaporation of tears from the eye surface. Also, we tend to stare and not blink as often when we are doing prolonged near activities, such as computer use. Thus, taking frequent breaks, and blinking more often, will certainly help. Occasional use of artificial tears (Optive, Systane, Blink) may be soothing.
Step 1. The biggest mistake made by Computer users is their lack of recognizing that high glare from the Computer screens is antagonistic to the EYES. Most Monitors have adjustment capabilities to reduce the brightness intensity and thereby the glare portion. Laptops are troublesome as the process is handled by tilting the screen for reduced direct glare in some cases. My personal example was serving time in a "Dark" Room Ambulance telephone incoming call center with screens with line on line of priority colored bands of account data. My trainer kissed me when her headaches disappeared after I lowered the intensity of her Monitor.
Step 2. Don't be afraid to visit an Ophthalmologist if this fails.
Two additional comments: be sure that your glasses prescription is current and correct for your driving needs. With your prescription, you are able to work at the computer without the glasses. Also, if the flashes/floaters increase suddenly, see an ophthalmologist for a dilated retinal exam.