What are those red lines on your eyes and can you have too many of them, because l think l have an abnormally high concentration of them?

Are you speaking of the blood vessels? Sometimes they can become inflamed due to allergies, dryness, etc. There are cases of abnormal growth of vessels due to certain conditions. Products such as Visine can shrink the vessels down and cause them to be less noticeable, but are not recommended for long term use. You should visit an Ophthalmologist if you are concerned. Good luck!