To answer your question, holding a grudge can be sinful. But to answer the real underlying problem here, I must tell you that based on the situation presented here and on details I edited out for the sake of privacy, holding a grudge appears to be the least of your problems.
Your girlfriend has experienced serious problems that are beyond your capacity to help, and which may contribute to her apparent inability to remain faithful. She might need professional help for those problems before she is ready to consider a romantic relationship with anyone. In addition to that, you both likely are too young for this kind of relationship and you have skewed ideas of chastity (by your own account, you probably are having sex outside of marriage, which constitutes fornication).
I can only recommend to you that you end this relationship immediately, and that you seek to become better educated about the Church's teachings on chastity. Catholic Answers' chastity outreach program Pure Love Club may be able to assist you further.