Ok, so I did what you said, text her something casual to be able to build more confort between us. We exchanged a few text but I didn't answer to the last one. I feel basicly that she thinks she's the big prize. It went like this :
ME - Hey I think I saw you yesterday. Not sure cuz you were not the crazy chick I met before
Her : And why is that?
Me : Well you told me two different reason lol (exboyfriend story and job).
Btw don't take it seriously it was a joke -.-
Her : Lol okay, it's all good
Me : At least feeling better today?

(not sure for the correct translation in english, but it looks like that)
Her : Yes lol...Slept all day! I think I was just really tired.
Then I didn't answer. The way she answered to the fact that she wasn't really fun shows like if she don't care by saying "It's all good"...
So I think the next time I'll text her will be the set up a date for the day after. I don't want to be the guy who will always text her first. :/ What do you think?
PS : It's an hb8-9 so PLENTY of guys were hitting on her, both night we met. But still we ended up together
so I feel like there is something between us but she's afraid of something. She told me she has been played before but I don't know if it's explain her behavior.
Your first mistake is that you had to clarify and justify yourself. NEVER do that. She can take it any way you want to and you're indifferent to that. That's what you want to project to women.
Your second mistake is that you are assuming too much. Nothing's happened, you guys exchanged four messages. Slow down that role. For now, focus on the moment with this girl. Also, establish big text threads. I've been texting with a girl for days on end. Single thread. Helps a LOT. She will say 'Oh! We are always talking!' and that's not a bad thing.