All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Whoever made a covenant with Allah to perform an act of devotion is recommended to fulfil it because He, The Almighty, Said (What means): "And fulfil God’s covenant when you made a covenant," {An-Nahl/91}.
He also Said (What means):"Among the believers are men who are true to the covenant they made with God. Some of them have fulfilled their vow, and some are still awaiting; and they have not changed in the least;" {Al-Ahzab/23}.
In fact, fulfilling a covenant is recommended; whereas, breaking it is disliked. This is especially if that covenant was made with Allah since He, The Exalted, Is more deserving to have His Covenant fulfilled.
However, if that covenant was intended as an oath then it is imperative to fulfil it for not doing so entails paying an oath expiation.
"If he said with Allah`s covenant, guarantee.......etc. These are metonymies. " In other words, it takes the ruling of an oath if he intended it as such. For more details in this regard, kindly refer to [Mughni Al-Muhtaj, vol.4/pp.320] and [Hashyat Al-Qailoobi, vol.4/pp.273].
Prayer of need, in principle, is a recommended act of Sunnah as agreed by the four Imams, and this is indicated in the following Hadith: Allah's Messenger (PBUH) said: "Whoever has a need from Allah, or from one of the sons of Adam, then let him perform Wudu', performing it well, then pray two Rak`ah, then praise Allah and say Salat upon the Prophet (PBUH). Then let him say: (La ilaha illallah Al-Halimul-Karim. Subhan Allah Rabbil-`Arshil-`Azim. Al-Hamdulillahi Rabbil-`Alamin. As'aluka mujibati rahmatika wa `aza'im maghfiratika, wal-ghanimata min kulli birrin, was-salamata min kulli ithmin, la tada` li dhanban illa ghafartahu, wa la hamman illa farrajtahu, wa la Hajatan hiya laka ridan Illa Qadaitaha, ya arham ar-rahimin) 'None has the right to be worshiped but Allah. Al-Halim (the Forbearing) Al-Karim (the Generous). Glorious is Allah, Lord of the Magnificent Throne. All praise is due to Allah, Lord of the worlds. I ask You for that which warrants Your mercy, and that which will determine Your forgiveness, and the spoils (fruits) of every righteous deed, and safety from every sin; do not leave a sin for me without forgiving it, nor a worry without relieving it. Or a need that pleases you without granting it. O Most-Merciful of those who have mercy." {At-Tirmidhi}.
In addition, Uthman bin Hunaif narrated that a blind man came to the Prophet (PBUH) and said: “Supplicate to Allah to heal me.” He (PBUH) said: “If you wish I will supplicate for you, and if you wish, you can be patient, for that is better for you.” He said: “Then supplicate to Him.” He said: “So he ordered him to perform Wudu’ and to make his Wudu’ complete, and to supplicate with this supplication: ‘O Allah, I ask You and turn towards You by Your Prophet Muhammad (PBUH), the Prophet of Mercy. Indeed, I have turned to my Lord, by means of You, concerning this need of mine, so that it can be resolved, so O Allah so accept his intercession for me." {At-Tirmidhi}.
Accordingly, if the covenant you (asker) have made with Allah was intended as an oath then you are obliged to fulfil it, and if you don`t then you are obliged to pay an oath expiation. However, if you didn`t intend it as an oath then it is recommended that you fulfil it.
As regards the question whether the prayer of need is an innovation or not, we believe that it isn`t since an innovation violates Sharia but this doesn`t. On the contrary, there are Sharia texts that prove its authenticity. We may add that the need you are praying for hasn`t been answered yet. We beseech Allah to make your task easy for you.
However, if performing this prayer daily is much of a burden then pay the oath expiation, and there is no harm on you if you stopped performing it. And Allah Knows Best.