You weren’t acting needy in sending that text message.
No, you didn’t need to wait for a couple of days before sending it.
She has already complained to you about how you take a while to answer her text messages. If anything, she would have hoped to have received more initial text messages from you by now.
She may have left your last message on “open” because she was worried that if she were to read it and reply, you would take a while to respond to her message yet again.
It is not needy to communicate regularly.
You only have to worry about neediness if you send her multiple text messages in quick succession because you are so eager for her to respond.
You haven’t done that so far.
Yes, there is a good chance that when she got sad over the fact that you take a while to reply to her text messages, she was indicating romantic interest.
Oftentimes, a girl wouldn’t really care about your response time to her text messages if she has no interest in you, unless you are a good friend of hers or her boyfriend.
You aren’t a close friend to her. Hence, there is a chance that her sadness was due to romantic interest, as she may see you as a prospective boyfriend.