What prophecy was about Timothy?
Timothy 1:18 This charge I commit unto thee, son Timothy, according
to the prophecies which went before on thee, that thou by them
mightest war a good warfare;
Both the Amplified and the Weust translations use the phrase "prophetic intimations" for the word "prophecies" in the KJV. This might mean that what was prophesied about Timothy was not specific.
Since Paul is citing them as a resource to use in bolstering Timothy for the work under difficulty that is before him, we might surmise that these prophesies were at least in general indicating a favorable report of the work Timothy was to do.
We know that Timothy had received a spiritual gift.
1 Timothy 4:14 Neglect not the gift that is in thee, which was given
thee by prophecy, with the laying on of the hands of the presbytery.
This may have been the gift of evangelism.
2 Timothy 4:5 But watch thou in all things, endure afflictions, do
the work of an evangelist, make full proof of thy ministry.
Timothy may have been inclined to put off the work to which he was called and in need of encouragement and exhortation.
2 Timothy 1:6-7 Wherefore I put thee in remembrance that thou stir up
the gift of God, which is in thee by the putting on of my hands. For
God hath not given us the spirit of fear; but of power, and of love,
and of a sound mind.
It would seem theat the "prophecies" about Timothy were not from the Old Testament but from the milieu of prophetic activity that was to be found in the early church.
1 Corinthians 14:3 But he that prophesieth speaketh unto men to
edification, and exhortation, and comfort.