Two pieces of advice from a veteran of the Lonely Hearts Club:
1. Learn to move on, man. Your latest map doesn't pan out? Move on. A girl rejects you? Move on.
2. Everyone wants their space. Even people in super-sappy love don't want to be with their partners everyday to some extent. You know the phrase, "Absence makes the heart grow fonder"? It's true. Learn it, love it, and embrace that thought next time.
Right now, you've been rejected, and you're still pestering this poor girl. If you want to try and still be friends with her, try not talking to her at all for a week unless it's an absolute necessity, like a fire. Starting right now. You made her cry, and she's probably pissed at you. You are most likely the last person she wants to talk to. You're probably thinking that you could apologize or comfort her, but she's not going to take it. In that week, you'll probably move on without realizing it.
Also, if you want to go out with her sister, go ahead with it, but maybe after a week or two. Don't be creepy by asking the first one if it's alright. There will be a big difference in response if you are already making her sister happy when you ask. And this goes into another general piece of advice: Don't fucking announce to the world/internet you have a girlfriend before you two are serious or are going after a potential girlfriend. That's a mindset no one likes in someone else. Change that right now.
And also, this is kinda more of a general point made towards the discussion in general, but I find being friends with a woman isn't bad, like Schwa stated. It's just being a decent human being. What is the worse thing is being friends with a woman that you haven't moved on over, aka "friendzoned". But you have to come up with your answer to those situations.
Also, funny story about women trying to not hurt us with rejection: One time, asked an old friend out via Facebook. Her idea of not hurting me? Don't respond at all. I knew she'd probably say no and it was pretty much a shot in the dark, but not responding made me feel like she didn't even respect me as a person at all. The friendship ended right there and then. (And yes, I did verify this with her.)