Thanks for writing to us.
A medium sized red spot on the outer part of the eye may happen due to a small capillary hemorrhage due an injury or a raised intraocular pressure
. An examination by an ophthalmlogist is essential to identify the cause. The systemic symptoms of dizziness
do need a systemic evaluation and blood investigations to find out the cause. These are not likely to be related to the red spot in the eye.
I hope this information has been both informative and helpful for you.
Dr. Rakhi Tayal