That Touch of Pink
(1962)

Philip (Cary Grant) wants an affair, Cathy (Doris Day) wants to marry.

Eventually, she succumbs to his charms and agrees to an affair, but every time they attempt to consummate the relationship, she breaks out in hives.

Eventually he succumbs to her charms and they marry, but on their honeymoon he is the one who breaks out in a rash.

Thanks Mary C!