(a) This section does not apply to a claim that is asserted by cross-claim, counterclaim, or third-party claim.
(b) A claimant may not institute an action under this subtitle unless:
(1) the claimant submits a written claim to the Treasurer or a designee of the Treasurer within 1 year after the injury to person or property that is the basis of the claim;
(2) the Treasurer or designee denies the claim finally; and
(3) the action is filed within 3 years after the cause of action arises.