Is my girlfriend’s reaction to me saying ‘I love you’ to someone else normal?

My girlfriend left me, for about a month, in July. During that time I met someone and had told them i think i might love you. After about a month, my girlfriend and i talked it through and I realized I wanted to be with my girlfriend, so I ended it with the other lady. My girlfriend found where I had messaged this other lady that and now refuses to allow me to tell her I love her, because, in her words, i had said it to someone else. Is this just her way of dealing with the situation or is this something more permanent?

Is my girlfriend’s reaction to me saying ‘I love you’ to someone else normal?
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