Where did that "revelation" come from? The Holy Spirit, I would say.
Correct.
Regardless, you didn't answer my question:
Why did Paul go "by revelation" to the Jewish Church leaders in Jerusalem to have his preaching examined and then approved (Gal 2)?
This next paragraph will answer all your questions concerning the difference between the apostles. Those that walked with Jesus under the law in Jerusalem and Paul.
Galatians 2:2
Then after an interval
of fourteen years I went up again to Jerusalem with Barnabas, taking Titus along also. It was because of a revelation that I went up; and I submitted to them the gospel which I preach among the Gentiles, but I did so in private to those who were of reputation, for fear that somehow I might be running, or had run, in vain.
But not even Titus, who was with me, though he was a Greek, was compelled to be circumcised.
There is a deeper point to this paragraph that you may miss, if you do not read it properly.
Paul had been an apostle for seventeen years. When Paul first became a Christian and an apostle which was three years before that period of fourteen years. Paul went to Jerusalem because God told Him to go for an obvious reason.
Paul knew the church in Jerusalem was following the law.
But not even Titus, who was with me, though he was a Greek, was compelled to be circumcised.
Paul was not in Jerusalem to have His ministry approved, because Paul had been an apostle for seventeen years. Paul is condemning the entire church in Jerusalem, that church was circumcising their converts. The Jerusalem church was following the law. Paul knew what was going on but the Jerusalem church was not under His authority. Paul could not directly rebuke that church as it was a Jewish church.
5 But we did not yield in subjection to them, even for an hour, so that the truth of the gospel would remain with you.
Jesus had Paul in Jerusalem for a reason. To witness the legalism of the Jewish apostles. This issue of legalism would explode in Antioch with Peter.
Why did Paul need his preaching approved and what authority did Peter, James and John have to approve Paul's preaching?
Paul did not need his apostleship, his authority over the Gentile churches approved.
6 But from those
who were of considerable repute (what they were makes no difference to me; God shows no favoritism)—
well, those who were of repute contributed nothing to me. 7 But on the contrary,
seeing that I had been entrusted with the gospel to the uncircumcised (Gentiles),
just as Peter had been to the circumcised (the Jews)
It is clear now that Paul's authority, papal authority, over all Gentile churches was confirmed. By the Jewish apostles.
The only explanation that makes sense to me is that Paul was under the authority of the Church leaders in Jerusalem.
Incorrect. Paul was directly under the authority of Jesus and Paul was the pope of the Gentile churches. Later, Paul would directly condemn Peter in Antioch. Because Peter was entering a Gentile church and that was under Paul's authority.