Does Baptism Wash Away Our Sins?

In this episode, Dr. Betters answers the question, "After our sins are washed away in baptism why do we all seem to be punished for sins we committed before coming to Christ? I traditionally tell people that what they are seeing isn't punishment it's actually part of suffering like what Paul went through after he done many of those same things to Christian's which was done to him. Jesus said come let me show you how much you must suffer. I tell them punishment for sin is hell nothing more nothing less. For sins after coming to faith in Christ we get chastening which hurts but again is not punishment or wrath. Am I correct or did I run in vain on that subject."