Is vowing to pray ten rak'ahs so as not to repeat a prayer due to obsessive-compulsive disorder considered a sin, and must it be fulfilled despite its futility in preventing the obsession?

One must reject obsessive thoughts and not pay attention to them, for they are among Satan's ploys to sow doubt in a person's beliefs and worship. It is recommended to completely turn away from these obsessions, seek refuge in Allah from Satan, recite the two Mu'awwidhatayn (Surahs Al-Falaq and An-Nas), frequently recite the Qur'an, and remember Allah. The Messenger of Allah, peace and blessings be upon him, said: "Indeed, Satan places his snout on the heart of the son of Adam. If he remembers Allah, he withdraws. If he forgets, he swallows his heart. That is the whisperer (waswas), the retreating one (khannas)."

As for the vow mentioned, it is a vow of contention (nadhr al-lajaj), which does not necessitate fulfillment and for which an expiation for a broken oath suffices. There is no sin upon the questioner because of this vow, but there is no need for it, as she might be unable to fulfill it or pay the expiation, thereby obligating herself to something she could have avoided.