All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
You described this relationship as ‘Haraam’ (unlawful), as such a relationship is impermissible to retain, regardless of whether or not it involved what you called a “physical relation.” Hence, this girl and her family did the right thing by refusing this relationship. If she wants to marry you, then you should have approached her Wali (guardian) to propose to her and then marry her, provided that her religiosity is generally satisfactory, meaning that she observes the obligatory acts of worship – especially the prayers – and keenly avoids grave sins. But if her religiosity is unsatisfactory, then you should disregard this matter and look for a righteous wife who would help you with regard to your religious and worldly affairs.
We would like to highlight a few points:
First: if a woman’s Wali unjustly prevents her from marrying a suitable suitor without a valid reason, then the Muslim ruler marries her off (i.e. acts as her Wali in the marriage contract).
Second: fulfilling a promise is recommended according to the majority of jurists and not obligatory.
Third: if you invested money into this forbidden relationship, then you should know that this is impermissible, and you brought loss upon yourself thereby.
Allah Knows best.