Let me quote some words of Jesus to encourage you: "With man this is impossible, but not with God; all things are possible with God" (Mark 10:27).
You see, God doesn't necessarily remove all our problems when we become followers of Christ–as your friend knows. But He has promised to be with us, and to help us and encourage us in the midst of those problems. Jesus' promise to His disciples is true: "Peace I leave with you; my peace I give you ... Do not let your hearts be troubled and do not be afraid" (John 14:27).
How is this possible? It is possible first of all because we are never alone if we know Christ. He loves us and is with us, and nothing we will ever face takes Him by surprise. It is possible also because His Holy Spirit gives us patience and joy, even in the midst of life's difficulties. It is possible as well because we know our problems are only temporary, and some day they will all come to an end when we enter heaven.
Which is better: to face life's problems and hurts without God–or to face them with Him? You know the answer. Ask Christ to come into your life today, and you too can begin to experience "the peace of God, which transcends all understanding" (Philippians 4:7).