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Sorry about your son's illness. In general, the eye muscle weakness including a sixth nerve palsy is due to the irritation
of the nerve(s), and should resolve slowly over few weeks with supportive treatment (including fluid hydration) of any dehydration complication of the hand, foot, mouth disease caused by a viral infection. The most important evaluation for the lazy eye
at this time is to exclude the presence of any other brain/eye abnormality including orbital lesion or secondary bacterial infection. The eye doctor should determine such possibility easily. So, I suggest that you take the child to the eye doctor for evaluation as soon as possible. The lazy eye will slowly resolved in few weeks. Patching the good eye for 3 hours each day can be beneficial by forcing the use of the lazy eye and recovery of eye muscle strength. In addition, I suggest that you instill preservative free tear drop such as Refresh plus or Genteal tear drop into each eye 4 times daily to improve corneal clarity and hence reduce blurred vision.
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Please note that this answer is for information only. It cannot be substituted for the visit to or the recommendation of your doctor.