Sometimes i have vein burst in my eye is it serious?

Depends where. : If a blood vessel bursts on the white part of your eye, that is the equivalent of a bruise and nothing to worry about. If you have a bleed in your eye , symptoms can range from seeing smoky floaters to vision loss.

Not likely: This is a very common occurrence and often seems to happen with a big sneeze. These go away with time and nothing needs to be done about them. As long as your vision isn't affected and you have no pain, you can ignore them.