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From About Face ID advanced technology - Apple Support

Even if you don’t enroll in Face ID, the TrueDepth camera intelligently activates to support attention aware features, like dimming the display if you aren't looking at your iPhone or lowering the volume of alerts if you're looking at your device. For example, when using Safari, your device will check to determine if you're looking at your device and turns the screen off if you aren’t. If you don’t want to use these features, you can open Settings > Face ID & Passcode and disable Attention Aware Features.

Have you tried rebooting your phone?

Try visiting your doctor and ask about your eye issues. They are NOT caused by the FaceID system and could be a sign of a serious medical problem. While doing that sell your iPhone, the X is holding its value better than any phone has.

What about toggling the involved settings on and back off?