Brief Answer:
Yes under stress an individual may develop strabismus.

Detailed Answer:
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Strabismus or Crossed eyes or Squinting eyes can occur due to a number of causes. Neurological causes, anatomical defects since birth, muscle paralysis etc are the common causes. It cause difficulty in binocular vision and in order to adjust for that eyes misalign themselves resulting in crossed eyes. Most common type of Strabismus is Constant Strabismus, but in some individuals they have Intermittent Strabismus.

Intermittent Strabismus is Strabismus occurring occasionally and under stressful situations like in febrile illness or stress. So yes, it can have psychosomatic origin but that is not common seen. Under stress individuals with intermittent strabismus can develop crossed eyes and few case reports also support this. But much detailed research studies are lacking. Even sleeplessness is also known to precipitate the strabismus.

Best treatment for this is Vision Therapy and eye muscle training and sometimes occlusion of one eye. This results in improvement in episodes. Relaxation exercises and reduction of stress result in improvement of symptoms. Reassurance is also found to be useful but mainly in children.

Thanks, I hope this helps you. Please don't hesitate to ask again for more doubts or if you need further clarifications in my answer.

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