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One cannot, of course, be 100% accurate about what is going on in another person’s mind, but that said, she is showing many signs of attention seeking and emotional insecurity.
Let’s look at her behaviour when you were in a relationship. She was not ready for that, but you moved on and saw other girls, which she then viewed as cheating. In other words, she was not ready to commit to you, yet thought the she had some proprietorial rights over you.
You did not cheat in that situation – you simply did what was normal and natural.
Since then, when you have met, she has behaved very strangely indeed, she punches and scratches you, does not want to sit next to you, and tries to break up your conversation with another girl.
It is most likely that she is too immature to form a good, strong and open relationship with anyone, let alone you.
Her behaviour (and it does seem attention seeking) shows that very clearly, and frankly, it is not a good foundation for a good bond being formed between you.
She may well change with time, but how long that will take is an open question. Are you prepared to put your life on hold for her until she does? If you are, then that’s fine. If not, keep moving on. Remember you are not responsible for her, and you have to look after your own interest.
Best regards, Norman.