Dude, that made me feel the exact same way. What also worries me is that maybe her "afternoon" proposal is so that she can keep things on more of a "friendly" basis with me. I don't know. When a guy says they'd like to see you and you don't mirror that sentiment back his way AT ALL, well, not impressed by that. Just saying. She could be totally different in person with me.
You went one
1 date. Take it easy bro. She may like you but is worried of coming on too strong. She may not want to scare you away.
Please don't use the line "squeeze you in". That sounds arrogant and rude. Just say that.
"That works for me. I'll pick you up at 4:00. Let's grab a drink (ice cream is too teeny bopper) and talk, walk by the lake, beach whatever."
Then see how she feels. On your talk be genuine. Tell her that you had a great first date. it was refreshing, that your last few dates have been disasters. Thank her for joining you this afternoon and that you'd like to have a real date and then give her your plan. Don't ask her, just say this is what I want to do next. Be assertive.
Don't give up hope over one text message. On your afternoon date you'll be able to figure out if she does like you or not. She just might be a slow mover, has shit going on in her life (imagine that!) and wants to take things slow.
Just make sure you don't leave her to the friend zone. That is why you need to tell her about how you liked that first date and want more dates, that you clicked. Be a man, don't gush your feelings but let her know you are a serious man.