Paul is not saying that we should check/prove/examine our works/"good deeds," to judge whether we are justified, for the Corinthians were one of the most carnal group of believers, and they would be given an "F." No, the context, is that there were many questioning Paul's apostleship. No, rather Paul's point was when he instructed them, "counter pointed" them to "examine" themselves, he was arguing, responding, to those who would challenge him, “examine” him.
1 Corinthians 9 KJV
1 Am I not an apostle? am I not free? have I not seen Jesus Christ our Lord? are not ye my work in the Lord? 2 If I be not an apostle unto others, yet doubtless I am to you: for the seal of mine apostleship are ye in the Lord.
3 Mine answer to them that do examine me is this,
Paul never doubted their justification, always referring to them as "saints," "brethren." . He wrote to them, because they doubted his Lord Jesus Christ given apostleship,
2 Corinthians 13 KJV
3 since ye seek a proof of Christ speaking in me, which to you-ward is not weak, but is mighty in you.
See it? See the dispute/challenge? See the context?
Survey "what cometh before" 2 Corinthians-the context. Thus, he argues, contends, that if these Carnal bunch of saints were “in the faith,” it served as evidence, proof, that he was, yes, an apostle, for he was the one that led them, "birthed" them, to the Lord Jesus Christ, per 1 Corinthians 4:15,
1 Corinthians 4 KJV
15 For though ye have ten thousand instructors in Christ, yet have ye not many fathers: for in Christ Jesus I have begotten you through the gospel.
1 Corinthians 9 KJV
2 If I be not an apostle unto others, yet doubtless I am to you: for the seal of mine apostleship are ye in the Lord.
That is, since("for" above-Paul is "connecting the dots") the carnal Corinthians were “in the Lord,” and “in the faith,” was concrete evidence,a "seal" of his rightful, authorized by God apostleship-again, 2 Cor. 13:3 KJV, and they should be convinced of such. Paul never argues that we are to look to ourselves, to "prove" we are saved, but look to the book, for our assurance.