I made a vow in my dream that if Allaah, the Exalted, relieved me of my hardship, I would wear the Niqaab (i.e. the face veil). Allaah, the Exalted, relieved me of my hardship; should I fulfill my vow that I made in a dream and wear the Niqaab?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

The deeds of the sleeping person are not recorded until he wakes up, as mentioned in the relevant Hadeeth. Hence, a sleeping person will not be held accountable for what he utters while sleeping. This means that if he commits Qathf (i.e. makes false accusations against someone), divorces his wife, apostatizes, makes a vow, or the like, it is not incumbent on him to do anything in this regard. The Prophet, sallallaahu ‘alayhi wa sallam, said: "The pen is lifted for three (i.e. it will not record their actions):  the sleeping person until he wakes up, the insane person until he becomes sane, and the young until he reaches puberty." [Abu Daawood and At-Tirmithi: Hasan]

Hence, such a vow is not considered a valid, binding vow, and you are not obliged to fulfill it.

As for the Sharee'ah ruling on wearing the Niqaab, it is obligatory on women to wear it.

Allaah Knows best.