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.
Whoever makes a vow to do an act that brings him closer to Allaah, the Exalted, such as fasting, is obliged to fulfill it. There is no scholarly disagreement in this regard. Allaah, the Exalted, praised His slaves who fulfill their vows. He says (what means): {They [are those who] fulfill [their] vows and fear a Day whose evil will be widespread.} [Quran 76:5-7] Allaah, the Exalted, also says (what means): {…and fulfill their vows …} [Quran 22:29] Moreover, the Prophet, sallallaahu ‘alayhi wa sallam, said: "Whoever vowed to obey Allaah, the Exalted, let him obey Him; and whoever vowed to disobey Allaah, the Exalted, should not disobey Him." [Al-Bukhari and Muslim]
Hence, it is incumbent on you to fulfill your vow, unless you are hindered by an excuse such as illness or a continuous inability. In this case, you are exempted from fulfilling that vow and should offer expiation like that of breaking an oath. However, once this excuse ceases to exist, you will have to fulfill your vow. May Allaah help you to be kind and dutiful towards your parents.
Allaah Knows best.