burst blood vessel in right eye
May be subconjunctival hemorrhage, can't say for sure without seeing it.
Hello and welcome,
What you are describing is most likely to be a subconjunctival hemorrhage. This happens when one of the small blood vessels burst due to increased pressure (coughing, sneezing, throwing up), or from irritation (rubbing the eye with your hand). Blood thinner medications can make it more likely too.
It usually takes a couple of weeks for the blood to be reabsorbed and the red area to clear, which will happen naturally.
Without being able to see this, subconjunctival hemorrhage is my best guess of what is going on.
If this is a recurring problem, be sure to see your doctor, and get your blood pressure checked and if on blood thinner meds, discuss that with your doctor too.
I hope this information helps. Please let me know if I can provide further information or clarification.