目線が左右に動くって英語でなんて言うの？

"目線が左右に動く" は英語で
gaze moves left and right
constantly look left and right
といえます。

2つパソコンのディスプレイ使っているので、目線が左右に動くけど、気にしないで下さい。
My gaze will move left and right since I use two computer screens. Please don't mind it.
Since I use two computer screens, I will constantly look left and right but please don't mind it.

少しカジュアルな言い方
Since I have two computer screens, I'll be looking left and right a lot so please don't worry about it.

気にしないで下さい。
- please don't mind it
- please don't worry about it