There are two possibilities;
Screens emit UV light which can damage corneal epithelium to certain extent which can be the cause of burning.
- this can further lead to dry eye which again causes burning sensation.
Most of the light which is less than 300nm (UV light) is being stopped by the cornea; more the UV light more the corneal epithelial damage;
Epithelium gets regenarated every 48 hours.
Omega3 fatty acids taken orally or topical lubricants will help in faster healing of epithelium.
Using UV protective eye glasses can help your corneal epithelium from getting damaged
Excessive near work too can cause burning; not burning actually but fatigue and tiredness.
Hope this helps :)
Follow up if necessary