Very good question. Thank-you for submitting it.
If you read the Book of Acts you'll see that Paul, after receiving the visions of Christ and further explanation of the Gospel, went to Jerusalem and inquired of the Apostle.
- He met with Peter, James, and John, to verify what he was teaching, and
- was given their blessing to preach the Gospel, primarily to Gentiles, although he would always start with the local Jews where ever he traveled.
At first, he traveled with Barnabas and was under Barnabas's discipleship. You'll initially notice this when the two were mentioned in the early missionary journeys. It was always Barnabas and Paul. They always listed the leader first when they wrote so you'll always see Peter and the Apostles: Peter, James, and John etc. Well, at first, we always read about Barnabas and Paul but . . . later it changes and we begin to read Paul and Barnabas.
When he first met with Peter, James, and John, although he submitted to them and was approved, he was instructed to go off to study and pray. Which he did. That's not to say there weren't some apparent disagreements, in particular between James and Paul, but those were caused by some who were distorting both the teachings of Paul and James.
Galatians recalls a dispute between Peter and Paul, because Peter was violating his own words spoken at the Jerusalem Council found in Acts Chapter 15.
The point is that Paul submitted to the Teaching of the Apostles and verified what the Lord told him, with them. Therefore, that gives us a scriptural assurance that St. Paul's writings and teachings were authentic and inspired. Indeed, St Peter references Paul's writings and authenticates them in one of his Epistles, noting also that they were difficult to understand. (2 Peter 3:14-16)
We also have assurances from Tradition. The Bible wasn't officially compiled into a single universally, accepted canon or book until the late 4th Century (382 A.D.). We had several versions of the Old Testament and many New Testament writings that were circulated from Church to Church.
When a Gospel or Letter arrived in the city, it was first sent to the Bishop, who compared the content with what he had been taught by his predecessor. If it was found to be doctrinally sound, then the Bishop allowed it to be read. Some of the Bishops came from Churches started by Paul, but many others were started by John, Peter, Mark, Thomas, Andrew, etc., etc. so we have a Living Tradition that confirms the Divine Inspiration of all the books found in the Bible, including the letters of Paul.
Finally, we have the Magisterium, the Teaching Authority of the Church, which is based on the Promise of Christ to protect the Church from Teaching error in matters of faith and morals. (Matthew 16:13-20)
This Magisterium comprises all the Bishops in union with the Bishop of Rome, the successors of Peter and Paul in Rome; in other words, the Pope. Jesus gave the Church the authority to bind and loose; that is, to make decisions guided by the Holy Spirit. See Matthew 16 and Matthew 18.
He promised the Gates of Hell would not prevail against the Church. The terms Gates has a very special meaning. The Gates of a city is where the Judges and Elders met to render judgment so the Lord promised that the Judgments and Councils of Hell would not prevail against the Church.
The Church's Magisterium met in several Councils, starting in 382 A.D. in Rome, then between 390 A.D. and 419 A.D. at the Council of Hippo and Councils of Carthage, guided by the Holy Spirit and based on Sacred Tradition, they gave us the Final Canon of 73 Books, which is the very same Bible Catholics use today. Later other other Councils, reaffirmed the same Canon every time it was challenged.
So we have a three-legged stool upon which we can sit securely in the knowledge that St. Paul's writings are authentic, true, and inspired by the Holy Spirt.
- The Written Word of God (the Bible)
- The Living or Oral Word of God (Sacred Tradition . . which itself is Biblical), and
- the Magisterium.
I hope this helps,
Under His Mercy,