Should I stop messaging her?

Situation: Shy girl I've met on online dating, we clicked since the first message and we kept talking every day. I tell her to go out on a date and she refuses because she's to busy so I just keep talking with her till she asks me out by herself and we go on a date.
The date is awesome, we find to have a lot in common, she looks likes she's really into me, keeps asking questions, she let her handbag near me when she goes to bathroom, we share drinks... when we go to separate she gives me a really strong hug and tells me she wants to meet me again.
So after it we start messaging again like everyday... the days fly and fly and she's still busy. When she's free, she's with friends or at home but she doesn't tell me to meet again and when I come with a date idea, she keeps telling me "ok but when I'm free" and after that we still messaging like everyday like nothing happened.

Now I feel like I'm just a chat buddy for her, she writes me back like everyday but refuses to meet again... What should I do? I thought about stopping the messages and talk to her after a few days with another date proporsal and if she doesn't want, just stop everything.
Should I stop messaging her?
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