Don't feel silly about crying over her. You love her, that's what you do when someone you love dies. I cry even when 1 of my fish dies.
I got my kitten Luna sorta the same way you got Binx. She was thrown out of a truck, in front of us. luckily she was in some type of a carrier, not a real cat carrier, more like a child's toy, but because she was in that, she didn't get seriously injured. She was more scared than hurt. Her biggest problem was the amount of fleas she was covered in.
When I first read your post I thought of Luna. When you posted that Binx died, that made me cry. I never met her and I cried for her. Don't ever feel silly crying over a pet. A pet is a friend, a family member, no matter if it's as big as a horse, or as small as fish.