Yes, I would certainly encourage you to talk with your pastor about baptism. Baptism is a public sign that you have now put your faith in Christ and are taking an open stand for Him.
It also is a sign that Jesus has now washed away all your sins. Think of it: You have been cleansed of every sin you've ever committed, because of what Jesus Christ did on the cross for you! You aren't saved because of anything you have done; you are saved only because you have put your faith and trust in Christ and what He has already done for you. The Bible says Christ "saved us, not because of righteous things we had done, but because of his mercy. He saved us through the washing of rebirth and renewal by the Holy Spirit" (Titus 3:5).
Let me add one other thought. No, you didn't grow up in a Christian family. But now you are part of one, because now you have countless brothers and sisters in Christ, and God is now your Father! Thank God for this, and ask Him to help you learn from them.
No matter who we are or what we have done, God still loves us and wants to forgive us if we will but turn in faith to Christ. This has been your experience–and it can be the experience of every person reading this.