Please, was Paul given a different dispensation from the other apostles?
The word "dispensation" means either a system of rules in place at a particular time or to be exempt from a system of rules. Thus, your question really is whether Paul taught a different gospel from the rest of the apostles. Such a claim is popular among Messianic Jews who live under the fantasy that they can keep the Old Testament laws and still be a follower of Christ. Paul's writings are clearly contrary to such a belief, so Messianic Jews try to relegate Paul's writings to be not applicable to them.
Paul mentioned a division taking place in Corinth in I Corinthians 1:11-13. People were using selected teachings from various men to bolster their positions. Though the people in Corinth were divided, the people they were citing were not divided. None of the apostles taught anything different from one another.
"Oh, that you would bear with me in a little folly--and indeed you do bear with me. For I am jealous for you with godly jealousy. For I have betrothed you to one husband, that I may present you as a chaste virgin to Christ. But I fear, lest somehow, as the serpent deceived Eve by his craftiness, so your minds may be corrupted from the simplicity that is in Christ. For if he who comes preaches another Jesus whom we have not preached, or if you receive a different spirit which you have not received, or a different gospel which you have not accepted--you may well put up with it! For I consider that I am not at all inferior to the most eminent apostles. Even though I am untrained in speech, yet I am not in knowledge. But we have been thoroughly manifested among you in all things. Did I commit sin in humbling myself that you might be exalted, because I preached the gospel of God to you free of charge? I robbed other churches, taking wages from them to minister to you. And when I was present with you, and in need, I was a burden to no one, for what I lacked the brethren who came from Macedonia supplied. And in everything I kept myself from being burdensome to you, and so I will keep myself. As the truth of Christ is in me, no one shall stop me from this boasting in the regions of Achaia." (II Corinthians 11:1-10).
Paul is declaring that his message is no less than any other apostle. Here "eminent apostles" or "chiefest apostles" refers to the weighting these false teachers were giving to the various apostles. If a statement by Peter could be misconstrued to appear to give support to a false doctrine, then those who advocated the false doctrine would declare that Peter was a more important apostle; so if another apostle, such as Paul, appeared to contradict Peter, then Peter's words carried greater weight. The flaw in the argument is that all the apostles were inspired by God, and they spoke not their own words but God's. Peter said, "But know this first of all, that no prophecy of Scripture is a matter of one's own interpretation, for no prophecy was ever made by an act of human will, but men moved by the Holy Spirit spoke from God" (II Peter 1:20-21). Paul said the same thing: "But I make known to you, brethren, that the gospel which was preached by me is not according to man. For I neither received it from man, nor was I taught it, but it came through the revelation of Jesus Christ" (Galatians 1:11-12). Or, as Paul said in another place, "If anyone thinks himself to be a prophet or spiritual, let him acknowledge that the things which I write to you are the commandments of the Lord" (I Corinthians 11:37).
Thus, either you deny that Paul was inspired by the Holy Spirit or you must accept that Paul taught the same teachings as every other apostle, "for God is not a God of confusion but of peace, as in all the churches of the saints" (I Corinthians 14:33).
It is true that Paul's mission was focused primarily on the Gentiles and Peter's mission was focused primarily on the Jews; however, both taught both Gentiles and Jews. Peter was the first to preach to the Gentiles (Acts 10). When Paul entered a new city, he generally first approached the Jews (Acts 17:1-4) and then went to the Gentiles. See: The Gospel of the Circumcision and the Uncircumcision.