Sorry to hear about your luck, especially with the blood flying into your face the first time. Hopefully you can get over it, and find peace in the fact that they likely didn't suffer. That, and the fact that it would've been hard to have avoided either.
I've never hit a bird, but I've come close a couple of times. Not on purpose, though. I did hit a raccoon years ago, because it ran out of the darkness and into my tire. I felt really bad. I don't know if I could control myself if I hit a dog, let alone a cat.
I don't trust birds. They like to bite me if they're pets (and what did I do? Nothing!). Also, when I took a family member to an appointment 30 minutes away 2 years ago, a seagull conveniently shat on my shoulder just as I exited the vehicle. Fucking thing.
I had been so lucky for my entire life up to that point.