Are they red like they're bloodshot, that is, you can see a web of veins, or are they solid red? If it's the latter, I'm surprised that you haven't run screaming to the doctor, because it's really disturbing looking, but it's nothing major. It's called a subconjunctival hemorrhage, but it's essentially just a bruise in your eye, probably from straining. But you say it's both eyes, which would be unusual, I think.

Of course, if it's webby, then I don't know.