What is the ruling on not covering the hair, given that I swore to cover it until it grows, and I did not specify a particular time or length, and a month has passed and its length has increased slightly?

Scholars agree that the swearer, in his oath, refers to his intention and purpose. The evidence for this is the hadith (definition): "Indeed, actions are by intentions, and indeed every person will have what he intended." If the intention is absent or forgotten, one refers to the "context of the oath" (bisat al-yameen) or the "reason for the oath" (sabab (definition) al-yameen), which is its motivation. Therefore, the questioner should consider the reason that angered her father, such as the type of haircut or the length of the hair, and wait until the effect of that reason dissipates or the hair returns to its normal length.