(a) On completion of a paternity proceeding, the court may order the clerk of court:
(1) to seal all papers in the case; and
(2) not to open any papers in the case, except on order of the court.
(b) In any further proceeding under § 5-1038 of this subtitle on support payments or custody, the papers in the case, once ordered sealed, shall remain sealed unless the court orders otherwise.