Is what was written on paper considered a vow, and is it obligatory to fulfill it despite not intending a vow?

A vow (nadhir) is not valid by writing alone unless it is accompanied by intention (niyyah). Merely writing, "If I do such and such, I will fast so many days," or "I will give such and such in charity," without the intention of making a vow, entails nothing. The verbal formulation (sigha) is an essential pillar, and writing takes the place of verbalization if it is accompanied by the intention of making a vow.