writing raw dialog

When you’re writing dialog it can be distracting if you have to constantly describe who is speaking it, it’s sometimes easier to write the dialog and explain who is speaking it later - I call this `raw dialog’.

This is a piece of raw dialog which I recently wrote. It’s a scenario from a story, a serialised erotic political thriller I guess you could call it.
This is exactly how I left it when I quit the writing session yesterday, this is exactly how it looks at the moment, I’ve written the dialog but there’s hardly any indication as to who is speaking it. The conversation was flowing (in my head) and I didn’t want to be distracted by having to write description. For your guidance, the dialog is between a girl who has fallen in love with another girl.
“What if you were to kind of fall into my arms?”
“Why would I want to do that?” Messie smiled innocently.
“Because - because it might be a nice thing to do.”
“Mmm. A nice thing to do. Lemme see. Nice in what way? Nice in the same way that it’s nice to fall into a boy’s arms?” she said teasingly.
“Maybe nicer.”
“Oh, I don’t think anything could be as nice as that. To have a boy’s strong arms around me, to feel his strong hard body pressing against me. To feel that -  urgency, pressing against me - ”
“Sassie, girls can have that urgency pressing against them, too.”
“I know, that’s what I just said.”
“No, I mean, two girls -”
“With one boy? I don’t think so.”