No, you haven't done anything wrong - not in God's eyes. In fact, you've taken the wisest and most important step anyone can ever take, by giving your life to Jesus Christ.
The most important truth I can tell you is that God loves you and knows what you are going through. He is with you every moment of the day, and you will never be alone when you know Christ! Jesus' promise is true: "Surely I am with you always, to the very end of the age" (Matthew 28:20). Your family may laugh at you or even reject you, but you are now part of a new family - the family of God. Remember: Jesus knew what it was to be rejected by an unbelieving world. He said, "If the world hates you, keep in mind that it hated me first" (John 15:18).
Does this mean your family will always be like this? No, not necessarily. Just as God reached down and touched your heart, so He can do the same with your family. Pray for them, and ask God to break through the barriers of pride and sin they have erected and open their hearts to the truth of the Gospel.
Don't argue with them, however, or become defensive or combative; that will only make things worse. Instead, ask God to help you demonstrate the love of Christ to them. They may not believe your words (at least at first) - but they can't argue with the witness of a changed life.