Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Since you made the said vow, you have to fulfill it as long as you are able to do so if what you conditioned the vow for takes place. Allah, The Exalted, and His Prophet (Sallallahu Alaihi wa Sallam) ordered us to fulfill the vow.
Allah says: "Then let them complete the prescribed duties for them, and perform their vows. (Al-Hajj 22:29) "
Allah further says when describing His noble slaves: "They (are those who) fulfill (their) vows, and they fear a Day whose evil will be wide-spreading. (Al-Insan 76:7)
The Prophet (Sallallahu Alaihi wa Sallam) said: "Whoever vows to obey Allah has to obey Him, and whoever vows to disobey Him should not disobey Him." Reported by Bukhari.
The Prophet (Sallallahu Alaihi wa Sallam) also said: "whoever makes a vow that he can fulfill has to fulfill it." Reported by Ashab Al-Sunan.
Fulfilling one's vow does not contradict sincerity, rather it is one of the signs of sincerity to Allah, The Exalted, as already mentioned in the verse about His noble slaves, where He mentioned some of the characteristics among which is fulfilling the vows.
There is no doubt that Allah is not in need of our acts of worship and is not in need of His slaves, as you have already mentioned, and it is something evident in religion and no one can deny it.
Allah stands not in need of any the Alamin (Mankind, Jinn and all that exists).
Allah says: "And whosoever strives, he strives only for himself. Verily, Allâh is free of all wants from the 'Alamîn (Mankind, Jinn's, and all that exists). (Al-'Ankabut 29:6)
But Allah legislated the fulfilling of a vow not because of being in need of it, but for the interest of the slaves themselves, in order to obtain much goodness and many rewards.
Allah knows best.