Short Answer

There is no specific wording you must use when asking Allah for something or sending peace on the Prophet. That is why scholars compiled books on supplications that righteous people used to make. However, it may be preferable to use wording similar to what the Qur’an and Sunnah used.

What the Scholars Said

Imam as-Sakhawi says: “Some have chosen other methods of sending blessings upon the Messenger of Allah…so this is an indication that there is leniency in the matter in terms of adding and subtracting words from the salutations and that they are not restricted to specific words or specific times. However, it is more virtuous and better to send blessings upon the Messenger of Allah with the words that he taught us.” (al-Qawl ul-Badi’, 89)

Advice

Be careful not to consider non-Prophetic supplications as prophetic. That would be lying against the Prophet. Some people insist on a specific method of supplication and give the impression that it was recommended by Allah or His Messenger, though it was not. This is a sinful innovation. Also, some people claim that certain supplication have worldly benefits like curing the sick or having good dreams. These benefits are the result of personal experience and may or may not be true for others. They should not be propagated as if they were guaranteed to have this effect, otherwise the Prophet would have taught it to us. If the benefit is referring to the Afterlife, such as “whoever says this supplication gets ten rewards”, then this is false because no one besides the Prophet could ever know such a thing.