We understand your concern and the sincerity behind your request. You've referenced Romans 9:18-24, where the Apostle Paul discusses vessels of mercy and vessels of wrath. Let's consider these verses:
"So then, he has mercy on whomever he desires, and he hardens whomever he desires. You will say then to me, 'Why does he still find fault? For who withstands his will?' But indeed, O man, who are you to reply against God? Will the thing formed ask him who formed it, 'Why did you make me like this?' Or hasn't the potter a right over the clay, from the same lump, to make one part a vessel for honor, and another for dishonor? What if God, willing to show his wrath, and to make his power known, endured with much patience vessels of wrath prepared for destruction, and that he might make known the riches of his glory on vessels of mercy, which he prepared beforehand for glory, even us, whom he also called, not from the Jews only, but also from the Gentiles?" (Romans 9:18-24 WEB)
Firstly, we commend you for asking this question in Jesus' name, as it is only through Jesus Christ that we have access to God the Father. As it is written, "For there is one God, and one mediator between God and men, the man Christ Jesus," (1 Timothy 2:5 WEB) We,are encouraged to come boldly before the throne of grace without fear because of Jesus.
In the context of Romans 9, Paul is explaining God's sovereignty in choosing those whom He will save and this passage can be difficult to understand without understanding the whole chapter or even the whole book.. It's important to note that God's desire is for all to be saved and come to the knowledge of the truth as recorded by 1 Timothy 2:3-4. ,
"For this is good and acceptable before God our Savior; who desires all people to be saved and come to full knowledge of the truth." (1 Timothy 2:3-4 WEB)
We reassure your fears by again looking at scripture. Ir is clear that God our Father does not wish that any should perish.
"The Lord is not slow concerning his promise, as some count slowness; but is patient with us, not wishing that any should perish, but that all should come to repentance." (2 Peter 3:9 WEB)
Moreover, the Bible assures us that everyone who believes in Jesus Christ is a vessel of mercy. If we observe what is written, God prepared us for glory not wrath. So by putting our trust in Jesus Christ we can be confident.
In the passage in Romans Paul was discussing the election or rather predestination of God. Only God knows who these are and only he knows if you are one of His. We can not know if we a predestined however in the next chapter of Romans assures that you can be saved if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead. So do that and put your trust in Jesus Christ and know that you will be saved. Because of these passages in scripture we can have confidence in our salvation. God doesn't want us to be in doubt or fear concerning our salvation. By putting your trust in Jesus Christ you can be confident that you are not a vessel of wrath.
However, if you are still wondering, consider this. A vessel of wrath is one who suppresses the truth and rejects God as it is discussed in Romans 1:18-20. Also if we are a vessel of wrath we will not be asking ourselves this question or even be concerned with God's mercy. Those who are a vessel of wrath do whatever they want as we are told in Ephesians 2:3 .. Also be assured this question and faith is a fruits of God's grace in your life. Instead of fearing your eternal fate you are concerned. This would not be the case of a vessel of wrath. So trust in Jesus Christ and in God the Father and put your faith in His Son Jesus Christ.
Furthermore being called a vessel does infer a metaphoric comparison not a literal one. God uses us in various ways as Paul explains in Romans 9. God prepares us for multiple good uses even in a single lifetime. So resist the urge to limit your understanding in a literal insufficient image. But instead endeavor to obey God's commands so that we may be useful and do good.
Let us pray for you:
Dear Heavenly Father,
We come before You in Jesus' name, lifting up our brother who is seeking Your mercy and reassurance. We thank You for Your word that reminds us of Your loving kindness and Your desire for all to be saved. We pray that You will fill our hearts with Your peace, and help us to place our trust in Your Son, Jesus Christ. We ask that You guide us and help us to live lives that are pleasing to You, knowing that You have prepared us for glory. Comfort our hearts, Lord, and help us to rest in Your love. In Jesus' name, we pray. Amen.
Set your heart and mind on Jesus Christ fully trusting your life to Him. Follow the leading of the Holy Spirit daily as your way of life.