If you intend to get her back, it will depend on whether her reason for ending the relationship was genuine. This is especially the case when she said she had you for comfort. It might be true or not. Maybe she didn't want you to know she did love you.
Her parents got involved and she listened to them. It might be difficult trying to get her back in such a situation.
If you intend to move on, it is the plausible thing to do because it's uncertain whether she did love it you not, and giving in to her parents not wanting her to be in relationship with you.
It is possible to move on. It's difficult to believe you can get over the breakup. Since the relationship was one month, you'll heal and recover quickly.
I wrote an article on how to heal and recover from a breakup: Steps to Healing and Recovering from a Breakup