What should I do regarding my vow to recite Surat Al-Baqarah daily so that so-and-so marries me, and should I continue reciting it, knowing that I did not adhere to it in the beginning?

The aforementioned vow is a vow of obedience and righteousness, and fulfilling it is obligatory. Therefore, one must continue reading the Surah daily, while making up for what was missed during the specified week. If the failure to fulfill it was without an excuse, then one must repent from that.