Yikes, that looks pretty painful! Poor Rylee.
And poor you... how horrible.
When Jackson was a pup, I had him outside on a leash when the farm dog (black lab) came down, seemed friendly, and snapped at Jackson resulting in a bloody nose. He scraped off part of his nose and I thought he would forever have a scar there but it actually went away. His mouth was bleeding, too, I think the dog had gotten his gums somehow and I just remember it bleeding forever (but not as bad as Rylee).
I hate blood, too, so I feel your pain. I hope Rylee gets better!