That feeling of pressure behind the eyes after screens is usually eye strain. Your focusing muscles are fatigued, you're squinting at glare or a too-bright display, and tension builds, often alongside a dull headache. It typically eases once you rest your eyes.
Relieve it with the 20-20-20 rule, matched brightness, less glare, blinking, good posture, and hydration. That said, persistent or severe pressure behind the eyes, especially with pain, vision changes, or nausea, can have other causes, so if it doesn't ease with rest and better habits, see a doctor.