Can a human get too much oxygen?

Fortunately the human body has Excellent regulating systems. Oxygen is carried in the blood by binding to receptor sites on the hemoglobin molecule in the red blood cell. There are only so many of these "handles" for the oxygen to adhere to. Once they are saturated, any additional oxygen the body is exposed to has no where to bind and will not be utilized

^That's not the full story though. Under normal and healthy circumstances, the haemoglobin will never become fully saturated, ie, those 'handles' should never fully be adhered to.

Full saturation is possible, however that is certainly what one would define as 'too much' oxygen. Hyperoxia, or Oxygen Toxicity can happen if a person was to inhale air with a much higher (or pure) concentration of oxygen. It is true that once the haemoglobin becomes 100% saturated, that no more oxygen can be utilised, but 100% itself is above healthy operation levels.

Oxygen toxicity can cause a variety of symptoms, including retinal detachment, seizures and breathing problems.

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Yes, you are right, this is especially true for infants who are born and placed on high flow oxygen. They are at high risk for loss of sight