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if it is just a blood vessel on the white of your eye then you need not worry as it does not indicate any major illness or disease in the eye.
If a small blood vessel bleeds in the conjunctiva, it leads to subconjunctival haemorrhage which is a relatively harmless condition and definitely does not indicate any other problem insided the eye. It generally subsides on it's own within 10 to 15 days with or without treatment(better to be left alone).
Unless this is associated with a severe pain in the eye / reduced vision you need not worry.
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These answers are for information purpose only and cannot be substituted for a check-up and visit to an ophthalmologist.