Yes burst blood vessels in the eyes can be caused by stress and high blood pressure.
When your blood pressure increases it puts more pressure on your eyes blood vessels including your eyes blood vessels.
When your eyes blood vessels get too much pressure that they cannot hold back then the blood vessels in your eyes can rupture and burst.
If your eyes blood vessels burst you need to get to the emergency room right away because it can lead to total blindness if let untreated.
Bleeding in the eye can lead to blurred vision at first and then later a complete loss of vision so always seek medical treatment when you have a burst blood vessel in the eye.
Also try to keep your blood pressure lowered and in a normal range and do your best to avoid stress as much as possible.