You need to contact your probation officer. Once the probation expired, if there was no motion to revoke filed, then the case is over. The state would have to sue you to recover the fees. However, if you did not pay the fees and the state wanted to do so, that would be a legitimate basis for a motion to revoke probation. And unfortunately no, if you pay the fees that will not stop the warrant, although the court is not likely to revoke you if the fees are paid.
Call your probation officer and ask for a copy of the final order dismissing your probation. You will learn then if there is such an order or if a motion to revoke probation has been filed. (If there is a motion to revoke your probation, you should immediately borrow the money to pay the fees off and you may have to hire a lawyer to go with you to the court with the money in hand to see if the lawyer can get the motion dismissed without you having to make a bond. If so, then the investment in the lawyer to avoid the bonding fee & going to jail is definitely worth the money.)