If you've prayed this prayer and are trusting Christ as your Savior, then the Bible says that you can be sure you have eternal life.
"...for, 'everyone who calls on the name of the Lord will be saved.' " (Romans 10:13).
"For it is by grace you have been saved, through faith–and this not from yourselves, it is the gift of God–not by works, so that no one can boast." (Ephesians 2:8-9).
"He who has the Son has life; he who does not have the Son of God does not have life. I write these things to you who believe in the name of the Son of God so that you may know that you have eternal life." (1 John 5:12-13).
Receiving Christ, we are born into God's family through the supernatural work of the Holy Spirit who indwells every believer...this is called regeneration or the "new birth."