No, the Bible doesn't say that someone who is rich can never go to heaven. In fact, some of the Bible's most faithful men and women were also wealthy (or at least prosperous)—people like Abraham and Job in the Old Testament, or Joanna and Lydia in the New Testament.
But the Bible does warn us about the dangers of wealth—and one of the greatest dangers is that it can keep us from God. Instead of putting God first in our lives, we put our money and wealth first, and end up ignoring God. We also can become proud, and we trust our money for our security. This is why the Bible warns us that "the love of money is a root of all kinds of evil" (1 Timothy 6:10).
Never forget that everything you have—your health, your abilities, your money, everything—has been given to you by God. Don't let money become your master, controlling everything you do. Instead thank God for what He has allowed you to have, and ask Him to help you use it wisely and for His glory.
Most of all, trust Jesus Christ alone for your salvation. No matter how good we are, or even how generous we are, we still fall short of God's standard—which is perfection. Only Christ can save us, and He will as we trust Him alone for our salvation. Put your life into His hands today.