A condom break is a risk, with or without the cut on your penis. However, a one-time vaginal event is extremely low risk, even if you were unprotected the entire time. Generally, PEP is reserved for people who have had a risk with a person known to be HIV+, or following high-risk events.
The choice of whether to take PEP or not is between you and your doctor. You may wish to consider the prevalence of HIV in your area before making the decision. If the prevalence is low, your odds against both encountering someone who is HIV+ AND getting HIV from a one-time vaginal event are astronomical.
Can you contact her to see when she tested last?