Can a lot of excessive time being in front of a tv screen cause droopy eyelids? If yes, can it be treated in some way? I'm only 20 years old.

No. There is no functional difference between tv viewing and video screen viewing such as on a computer. If there were a relationship causing droopy eyelids, we would be in the middle of an epidemic. You are young to have the older age eyelid type of drooping, so best to get a quick check with your ophthalmologist to determine why this has occurred and to recommend remedies.