Where do you draw the line between showing interest vs exhibiting needy behavior?

I've gone out with a girl a few times and last week(3rd date), I slept with her at her place. I may have a minor case of one-itis here, but I am fine with it since I see a long-term potential here. I am still speaking to other girls, setting up dates, hooking up with an FWB who lives in the next building. I'm not holding my breath out for this one girl until there is a "Fuck yes" from her.

BUT, I've caught myself exhibiting needy behavior(over text) in the past few days.

I can say with certainty that she invests in this potential relationship. While I paid for the first date, she paid for the last two, made sure her apartment was squeaky clean before I came over, cooked some snacks for me, made sure I was very comfortable, very energetic in bed and wanting to please me, always complimenting me on looks, intelligence, popularity, etc. I left her house in the morning when she said she wants to see me next week.

One thing to note here is that she takes hours to reply to my texts although I'm sure she checks her phone all time (courtesy - Snapchat)

She said she isn't feeling well mentally due to work and wants to be present when we hang out -- I offered to speak with her and be her therapist She expressed problems with her job -- I gave advice on how to talk with her boss(I have more work experience than her) I invited her for dinner on Mon, she said she would get back to me(this is where being present when we hang out came along) but never did -- I checked if she's doing well that night when I didn't hear back from her. When she didn't reply for a long time -- I ended up calling her which went unanswered. BIG MISTAKE I asked her how her weekend schedule looked like and she said it looks busy -- I asked her when she's free and yet to receive any response

Every time, I consciously prevent myself from exhibiting needy behavior, but I feel I am crossing the line here. Sure, I see a long-term potential here but then, I am getting myself into the state of one-itis without the girl (probably) being very sure about me.

Am I exhibiting needy behavior? Am I just showing concern for her/showing interest in her? Am I just nagging her?

For someone relatively inexperienced like me, I don't know where to draw the line between showing neediness and showing genuine interest without coming off as needy.

Any advice would be very helpful!