For the last four months, every 2-3 weeks, the sclera of one of my eyes turns blood shot red (a broken blood capillary). what could be the reason?

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.