Actually, in Acts 15, Paul taught the other Apostles, who learned his Doctrine.
Paul's Doctrine, came from Jesus, so, no other apostle was going to "check this" or "correct this", as Paul's Doctrine was given to Him by Jesus., personally., including THE Gospel.
Galatians 2:1-2
1 Then after an interval of fourteen years I went up again to Jerusalem with Barnabas, taking Titus along also.
2 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 I might be running, or had run, in vain.
Paul here indicates that he submitted the Gospel he was preaching to the Elders/Apostles at Jerusalem for inspection. His concern, as he says plainly, was that he feared he had "been running in vain," or had been preaching a false Gospel. And so, he offered to the apostles what he understood of the Gospel and the doctrines of the faith so that they could set him right on these things, if that was needed.
Galatians 2:7-9
7 But on the contrary, seeing that I had been entrusted with the gospel to the uncircumcised, just as Peter had been to the circumcised
8 (for He who effectually worked for Peter in his apostleship to the circumcised effectually worked for me also to the Gentiles),
9 and recognizing the grace that had been given to me, James and Cephas and John, who were reputed to be pillars, gave to me and Barnabas the right hand of fellowship, so that we might go to the Gentiles and they to the circumcised.
After getting a good idea of what Paul was preaching and convinced it was of God, James, Peter and John extended to Paul the "right hand of fellowship," formally sending Paul as a minister to the Gentiles, as they were ministers to the Jews.
Acts 15:2
2 And when Paul and Barnabas had great dissension and debate with them, the brethren determined that Paul and Barnabas and some others of them should go up to Jerusalem to the apostles and elders concerning this issue.
In order to settle the debate between Paul and Barnabas, the brethren sent the two men to the apostles (James, John, Peter) at Jerusalem. They did this, of course, because these apostles held high authority in the Early Church, "first among equals" you might say, and were recognized by the Early Church to possess such authority - even over Paul and Barnabas.
Acts 15:4
4 When they arrived at Jerusalem, they were received by the church and the apostles and the elders, and they reported all that God had done with them.
Paul and Barnabas gave a report of their doings to the apostles and elders at Jerusalem, suggesting that Paul and Barnabas were, in some measure, under the spiritual authority of the apostles at Jerusalem. And in Acts 15, only statements by Peter and James during the council are recorded (none by Paul), both of a directive sort, and Paul is given a letter from James to deliver to the Gentile Christians at Antioch stipulating things the Gentile believers were not to do (fornication, eating things offered to idols, blood, or animals that had been strangled to death). All of this is strongly indicative of Paul being under the spiritual aegis of the apostles at Jerusalem, in particular, as the Early Church, in general, seemed to be.
In light of all this, I wonder at your statements in the quotation above.
In Galatians.......... Paul speak about the other Apostles, and their knowledge and said this.. about them all...
""""""As for those who were held in high esteem—whatever they were makes no difference to me; God does not show favoritism—they added nothing to my message."""""""
And in 2nd Peter, .. it was Peter himself who said that Paul's letters were "Scripture"......equal to the Torah.
Later these same became the doctrine for the Church, and THE Gospel, and they make up MOST of the New Testament Epistles.
Yes, I've already noted in an earlier post that Peter referred to Paul's writings as "Scripture," but the things you point out here don't somehow dissolve all that I pointed out above. You can be sure that if Paul had diverged from what Peter, James and John understood and taught of the Gospel and they had rejected Paul as a fellow apostle, Paul would have been rejected by the entire Early Church, too.
As Paul demonstrated, the sinful partiality he saw among the Jewish believers he was right to challenge, even when it meant challenging Peter directly. But, in general, Paul operated in deference to the apostles (and elders) at Jerusalem, as the scripture I cited above reveals.