The most likely diagnosis, based on the description, is a subconjunctival hemorrhage.
Further Explanation:
Since the patient denies having any type of trauma or injury to the eye a corneal abrasion can be ruled out. The patient is not having any visual disturbances, pain, or discharge that can rule out conjunctivitis, and acute iritis. This leaves the doctor with the conclusion it is a subconjunctival hemorrhage.
A subconjunctival hemorrhage is caused when the small blood vessels in the eye break. This can be caused by forceful coughing. Since the patient has stated he has been coughing and has had a cold this will be the reason for the broken blood vessels in the eye. The red spot in the left eye is actually bleeding that is showing. It is harmless and will heal on its own after a few days.
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