Another broken blood vessel or something from straining. something wrong with my eyeball vessels?

Unlikely: You may have a slightly weakened vein on the surface of the eye which responds to strain, coughing or sneezing by leaking a tiny touch of blood. Unless you have a clotting problem (do you bruise easily? Are you bleeding elsewhere?), you don't have to worry about a bit of blood on the white of the eye which looks dramatic but is usually benign.

Bleed: This is a sub-conjunctival hemorrhage. As long as the vision is unchanged and there is no pain, everything should be fine. If it is a little irritated, then you can use an artificial tear up to 4 times a day to lubricate. This is due to a blood vessel leaking blood and is usually without cause. Sometimes straining or blood thinner can cause this. If it continues to happen, follow up with eye md.