Good question. I’ve copied a footnote from my lesson on the text in Galatians 1 which addresses your question:
35 Paul’s account of his first visit to Jerusalem does not conflict with that of Luke in Acts 9:26-30. Luke tells us that Paul fled to Jerusalem from Damascus, attempted to associate with the “disciples” there (Acts 9:26), and was shunned until Barnabas took him to the “apostles” (9:27), after which he was free to come and go with them among the believers (9:28). Paul informs us that it was only Peter and James who were present and with whom he met and then ministered. The brevity of this visit is not inconsistent with Luke ‘s report, which tells of a death plot and another escape. Both accounts then describe a journey to Cilicia, where Tarsus was located (compare Acts 9:30 and Galatians 1:21).
(from Lesson 5 in a series on Galatians found here: /docs/nt/books/gal/deffin/gal-05.htm)
The Bible Knowledge Commentary says,
The point of Paul’s declaration is clear. He formed his theology not by consulting with others, but independently as he sought God’s guidance. 1:18-20. Paul then reinforced his previous argument by asserting that he waited three years after his conversion to go to Jerusalem, time that was spent in Arabia and Damascus (v. 17). Would he have waited that long if he had needed theological instruction from the disciples? When he did go, it was to get acquainted with Peter, that is, it was a personal visit lasting only 15 days. Paul then left because of a plot against his life (cf. Acts 9:29). Meanwhile Paul had had a meaningful time coming to know the noted apostle, but there is no suggestion that Peter gave him theological instruction or apostolic endorsement for his ministry. Of the rest of the apostles Paul met only James, the Lord’s brother, a leader in the church in Jerusalem (cf. Acts 12:17). To stress the truth of what he had just said—no doubt in the face of a Judaizer’s charge that he had misrepresented his relationship to the apostles—Paul put himself on oath, calling God to be his witness that he was telling the truth.
Walvoord, John F., and Zuck, Roy B., The Bible Knowledge Commentary, (Wheaton, Illinois: Scripture Press Publications, Inc.) 1983, 1985.