Is it permissible to recite the supplication, "Turūd Tunajjīnā" mentioned in the question, and is its narration authentic?

This form of prayer upon the Prophet, peace and blessings be upon him, is an innovation and was not mentioned in the Sunnah. Al-Safuri and Al-Fakihani mentioned it based on a dream, and it is well-known that rulings and the virtues of deeds are not established through dreams. The religion of Allah is complete, and a Muslim does not need to legislate an act of worship based on visions or dreams.

It has been authentically reported from the Prophet, peace and blessings be upon him, that he used to say certain supplications during distress, such as: "There is no god but Allah, the Almighty, the Forbearing. There is no god but Allah, Lord of the heavens and the earth, and Lord of the Magnificent Throne," and "O Ever-Living, O Sustainer, by Your mercy I seek aid."

A Muslim should be keen to follow the Prophet, peace and blessings be upon him, and not innovate in religion, as Abdullah ibn Mas'ud said: "Follow, and do not innovate, for you have been sufficed."