I Have An Eye Problem: As I Was Rinsing Some

I have an eye problem: As I was rinsing some bleach out of my hair, I think some of the run-off may have gotten into one of my eyes. I rinsed it thoroughly. There wasn't much of a burning sensation (I actually think that rinsing it may have made it more uncomfortable...), it's just a bit red. The white part isn't even red though, there's just some veins/capillaries that are more visible. I'm just a bit concerned, because the emergency room is rather costly, and I don't want to pay for a useless visit. Again, there is no burning or blurred vision, just some inflamed capillaries. It also wasn't direct contact with bleach, just some run-off water that may have contained bleach...