You are having a sub conjunctival hemorrhage. Don't worry it will go on its own in about 7 to 10 days.
Next Steps
Although subconjunctival hemorrhage is by itself not dangerous. You need to get your eyes screened for other internal damage the I jury could have caused like retinal holes, glaucoma etc.
For daily computer use for prolonged hours, you can start using artificial tear drops every 1-2 hours while working on computers.
Health Tips
Watch out for decrease in vision, black spots in your vision. These are symptoms of retinal damage.