If you were not arrested, as of right now you have no record. The police may forward the case to the State attorney for prosecution at a later date or they may have decided with the stores cooperation that payment of the civil fine was sufficient. The State, assuming the value of the items was less than $300 and you have no prior thefts, can file charges within 1 year pursuant to the Statute of Limitations. Good luck.
You do not have a criminal arrest record per se. But likely the police filled out a FIR which is a record in their files. Also, if they file the report with the State Attorney's office, you could get charged and brought to court via a warrant or a summons to appear. Call a lawyer to contact the prosecutor's office to see if they have opened a case on you. The lawyer can check and see if the state has a charge and if they intend on filing on it. good luck!
If charges are filed, a warrant will issue and you will be arrested, or a summons will issue instructing you to come to court. At this time, you do not have a record nor charges but that does not mean that charges will not be filed.
As far as the civil fine, that is a separate situation. It does not matter that you paid (or if you refused to pay) the civil fine (although I guess that if a prosecutor is aware that you paid and you cooperated fully and the amount stolen was little then you could get a bit of the pity factor regarding charges.)