According to your present complaints it seems to get severe through the day following a long time exposure to screens. The irritation most probably could be because of Dry Eye disease. I suggest you could limit your exposure to screens apart from your work time and you could take 20 second breaks in between work time and look at something a far atleast 20 feet far. You could decrease the brightness of your screens. Hot compresses with warm packs should help. Eye massages and eye exercises and most importantly check for lack of sleep. I suggest you can clean your lid margins with diluted baby shampoo scrubs.

It seems to be a conjuctivitis with possibly lid margin involvement

Can you send photo ? How much area of the eye was red - full or one section only ? Is your vision blurry ?

Continue nefacool eye drop and for irritation start eye drop optive 4 times a day in both eyes.Do work on screen with frequent breaks.Your issue will be resolved within a week. Thanks

It takes a week or 2 for the subconjunctival hemorrhage to resolve.You can increase the frequency of the drop.That will provide relief.