Now that your a christian you feel like you should pay for the stolen items from the store. It is my advice to not take money to pay for the item that was stolen. Do not tell them what you did. Keep that between you and Jesus.
You might not know, that the store has a special price on the items they sell to cover lost and stolen items. That means the item you stole is already paid for. You probably paid for it yourself 100 times by shopping there.
Here is the real problem with turning your self in. You could go to jail and face very high fines. The store owner, maybe even the store employee will turn you over to the police. After that you will face a judge, receive fines and jail time. You could also get sued to add onto it.
The world is unforgiving, and by being with God you have made the world your enemy. The world wants to destroy you because your with God. Jesus already paid for your sins. Making atonement will not help you.