If a girl does not initiate anything does that mean she is not interested?

Anonymous
So there is this girl I have known for a long time and recently had a crush on. I asked out her out and we only went on a few dates before she had to go back to her hometown for the summer. (We are in uni btw) I really like her but the problem is that she does not initiate any sort of physical contact during the dates and seemed to be uncomfortable when I try to initiate any; she only let me put my arm around her shoulder once. Now that she is away she never text or message me first. I always have to text her first but when I do she responds and we can end up texting for hours. She is pretty conservative and so am I and I don't know if that is what is causing her to act reserved.

Anyways I am just wondering if she is truly interested since she has never shown any signs of interests; but if she is not interested why would she go out with me in the first place? Should I give up or should I keep on texting her first until she comes back at the end of the summer?
If a girl does not initiate anything does that mean she is not interested?
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