Long story short, I met a girl while out a couple of weeks ago. We danced, made out, and exchanged contacts. One day after that I messaged her and asked her to join me for a walk a couple of messages in, which she declined because she had to study for the final exams we had coming soon. I shrugged it off, said it's cool and then we messaged for a couple of days after that. We had a great conversation over text and a couple of days after that I hit her up again, inviting her to join me outside for ice cream, this time she says she is out of town for the weekend so she can't. I suggest we do it some other time, and she responds with "Okay then, I'm sorry". I haven't messaged her since, because she has already somewhat turned me down twice, wanting her to start a conversation this time but that never came. I'm getting mixed signals because she recently liked a photo of mine on Instagram and I don't know what to do.

Has she lost interest? Do I dm her again? I don't want to be the one that always starts the conversations and I'm afraid of coming off as needy.