Why does under my left eye twitch nonstop?

Different causes: Sleep deprivation & medications could be likely culprit. Usually not harmful.

Stress: Twitching of the eyelids is usually caused by some form of stress - emotional or physical. It is often difficult to pinpoint the exact cause. The twitching will ultimately stop, but can take weeks to do so. Rest, artificial tears and cool compresses may help speed recovery. If the twitching is severe and/or painful, see an eye doctor.

SOD: Energy depletion causes eye to twitch to replenish eye energy use superoxide dismutase in high doses 10, 000 units 4 -5 times a day until twitching stops. The other formula that works - zeaxanthine and lutein.

Myokymia: You are describing myokymia - an involuntary twitching of the skin around the eyelids. It's believed to be related to lack of sleep, stress, and caffeine use. Change these risk factors and it should abate.