Hi Tuo,
As you will know, 3 months into a relationship can be a pretty intense time. Your girlfriend was probably going through a big emotional change, and facing the prospect of really falling for you deeply. This type of deepening in the relationship would have sparked a number of questions in her mind. Is this the one? Is this someone I could live with, or even bring up children with?
As such, she may have faced, for the first time, the prospect of telling the world about her sexuality. Of course, you are in the same situation, but we all react to things differently. It may be that she's explained things to you exactly as they are: She knew that if the relationship were to continue her sexuality would, inevitably, have to become common knowledge. She was terrified of this, but her love for you overcame that terror!
I would welcome her back with open arms, and show as much compassion as you can for the huge psychological change and period of growth she is experiencing. In a complex relationship like yours, this type of selfless support will be necessary in the years ahead You are a blessing to each other.
However, if it continues, and she keeps being flaky, then you will have to ask yourself if the balance of positive to negative is right for you at this stage in your life. You may have to leave her, but I would suggest not yet
Good luck, follow your heart and things will work out for the best
Love one another, but make not a bond of love:
Let it rather be a moving sea between the shores of your souls.
Kahlil Gibran