No, this isn't necessarily true. The Apostle Paul was the greatest Christian who ever lived, and yet he suffered from some type of recurring illness that caused him great difficulty (see 2 Corinthians 12:7-10).
It's true, of course, that when we deliberately abuse our bodies (with things like alcohol or drugs or sexual promiscuity or overeating) we'll pay a heavy price, both physically and emotionally. God gave our bodies to us, and when we ignore His laws and treat our bodies with contempt, the inevitable result will be injury or sickness, or even a shorter life. The Bible commands us to take care of our bodies, and when we fail to do this, we are failing to do God's will.
But not all sickness can be traced to a specific sin we've committed. Sickness and death affect us all, and the reason is because sin -- like a deadly virus -- has invaded the whole creation. We live in a fallen world, and decay and sickness and death are the result. The Bible says, "For the wages of sin is death" (Romans 6:23).
Build your life on a solid spiritual foundation -- one that will last, no matter what happens to you. That foundation is Jesus Christ, who came into the world to rescue us from sin's guilt and power. Make it your goal to live for Him. The Bible says, "Physical training is of some value, but godliness has value for all things, holding promise for both the present life and the life to come" (1 Timothy 4:8).