If there is a perforation in the ear drum it is advisable to get operated to prevent further problems. This is not an emergency surgery and is done when the ear is dry and has no infection.

She has Mastoid infection Mastoiditis with Perforation, the options are to take treatment for few weeks and proceed for surgery if problem does not resolve with medicines, this is my opinion, some will suggest Surgery right away as disease if uncontrolled can progress during treatment. These are 2 therapeutic ideas and both are correct.