Is eternal life in heaven a reward to be earned?

No, salvation is not a reward for anything you do on earth. It is a gift from God and nothing you can work for, but only receive from Him by the power of the Holy Spirit. Please see in scripture Ephesians 2:8 For by grace you have been saved through faith, and that not of yourselves; it is the gift of GOD, not of works, lest anyone should boast. (Eph. 2:9 also).