Yes, we're all different in our personalities, and surely one of life's greatest challenges is learning to get along with people who are different from us. On the other hand, have you ever thought about how dull life would be if we were all exactly alike?!
Does this mean we can never change, or that even the rough edges of our personalities can never be smoothed away? No, of course not -- especially as we face them and seek God's help to overcome them. I think, for example, of the Apostle Peter in the New Testament. He was one of Jesus' most devoted followers -- but at times he could be impetuous and even cowardly, denying on one occasion that he knew Jesus (see Luke 22:57). But toward the end of his life Peter was a much different man, as we see in his letters.
Take your own situation as an example. You may never become the happy-go-lucky, carefree person your sister seems to be, but you can become someone who faces each day with optimism and freedom from constant worry. The key is to learn to trust God and His love, instead of your feelings and fears.
Begin by asking Jesus Christ to come into your life -- beginning today. Then when worries begin to flood your heart and mind, turn them over to God in prayer and trust each situation into His hands. The Bible is filled with God's promises; discover them and learn to trust them. The Bible says, "Great peace have they who love your law, and nothing can make them stumble" (Psalm 119:165).