Don't self-medicate or ignore the burning if it gets worse - what you're describing is super typical from spending hours staring at screens, it's called digital eye strain, and while it's normal, you should definitely go see an ophthalmologist to rule out anything more serious like dry eye or a refraction problem that the screen is making worse.
In the meantime, try the 20-20-20 rule: every 20 minutes look at something 20 meters away for 20 seconds, keep your computer at eye level, and don't forget to blink more than you think you do (people who work with screens blink less without realizing it, it's wild!).