New South Wales
Another important pair of rules quote to show that you do resolve all the cards before going Insane or becoming Wounded are listed in the Damage & Horror section of the rules:
RRG - Damage & Horror wrote:
• If an effect cause an investigator to suffer Damage in excess
of his health, he suffers all Damage from that effect before
becoming Wounded and discarding his facedown Damage.
• If an effect causes an investigator to suffer Horror in excess
of his sanity, he suffers all Horror from that effect before
becoming Insane and discarding his facedown Horror.
In both cases, this lets you know you complete resolution of whatever effect caused you to draw Damage/Horror before triggering the Insane/Wounded effect. This would include cards that force you to draw even more Damage or Horror when they resolve.