No, it isn't inevitable that you'll follow in your father's footsteps; God didn't make you so you'd have to do what he did.
Instead, the Bible makes it clear that each of us is responsible for our own actions. We can't blame someone else (including our parents) for what we did, or say that we had no choice in the matter because God made us that way. Each decision we make is ours alone, and we alone are responsible for the choices we make -- either good or bad. The Bible says, "The soul who sins is the one who will die. The son will not share the guilt of the father" (Ezekiel 18:20).
This doesn't mean it's been easy for you to choose the right way -- for it hasn't. Your father left you a poor example, and never showed you how to live a better life. But I hope you'll take your brush with the law as a wakeup call -- a God-given opportunity to start anew and put your feet on a different path, with His help. God loves you, and He doesn't want you to end up the way your father did.
How can you do this? The key is to put your life into God's hands, by committing yourself to Jesus Christ. By a simple prayer of faith ask Christ to forgive you and come into your life today -- and He will.