Did i cross the line w/ my professor?

I've had students say more familiar things than that to me, and I wasn't offended. (I WAS offended by some things students said to me, but not that kind of thing!) It sounds as if you and this professor have a good relationship and she cares about your academic and professional future, since she said that you could do something for HER by getting yourself an internship. I hope the "Thanks, I'll see you then" part of your message referred to her offer to sign the papers and that you'll go. If you're not even sure that your last email was delivered, you can just not mention it--simply ay that you appreciate her offer and are there to take her up on it. Bur I really don't think anything so trivial could have damaged your relationship with her.