It is not at all likely to be a "popped blood vessel" most likely it is a benign vascular growth called a "angioma". See an Eye MD for a definitive diagnosis.
Ask your family MD to refer you or go to www.geteyesmart.org
Thanks for answering! But I just googled what angioma looks like, and my case looks more like a popped blood vessel. It's on the white part of my eye. And the blood vessels are pretty visibly clumped together.
This sounds a lot like what i have. I have a large and visible blood vessel running from my tear duct to the iris, on both eyes. I've researched on the internet but have found nothing that explains what it could be. Ophtalmologists i've been to say it's conjuctival allergies, and the prescribed drops soften the redness of the blood vessels a little bit, but it doesn't go away. I've had this for at least 8 years now. It looks awful.