Christians get sick just like everyone else, and they have problems just like everyone else; God hasn't promised to take these away. The Apostle Paul endured a long and painful illness, and repeatedly asked God to take it away - but He didn't (see 2 Corinthians 12:7-10). We live in a world that has been ravaged by sin, and we share in its troubles.
But God has promised to be with us in the midst of our troubles - and that is a wonderful truth. Jesus said, "In this world you will have trouble. But take heart! I have overcome the world" (John 16:33). Even when life isn't the way we wish it was, Christ is with us, and that gives us comfort. Which is better: to face life's problems alone, or to face them with Christ? He knows what we are going through - for He also endured pain and sorrow.
No, your sister's faith hasn't kept her from troubles - but it has kept her from despair. I suspect her troubles have also made her faith grow deeper, giving her new strength to endure. The Bible says, "We know that suffering produces perseverance; perseverance, character; and character, hope" (Romans 5:3-4).
But troubles point us to an even greater truth: Some day, our lives will be over - but if we know Christ, we know we will be with Him in heaven forever. Our troubles are only temporary - and ahead of us is heaven. Is your hope in Christ?