What should the questioner do, as she swore six years ago not to marry a certain person, but she does not remember who that person is, and she suspects that her current husband is the one intended by that oath, while he denies any knowledge of the matter?

You are not required to do anything if the marriage takes place while forgetting the oath, or being ignorant that this man is the one the oath was sworn upon, based on the hadith: "Mistake, forgetfulness, and what they are coerced into, have been lifted from my nation."