Is it obligatory to wash away madhy if it is mixed with urine resulting from urinary incontinence, when there is uncertainty about its cause (incontinence or arousal)?

The Lawgiver's pardon for the impurity of a person afflicted by incontinence ( سلس - سلس البول أو الغائط - continuous discharge of urine or feces) is specific to acts of worship (عبادة), because there is no benefit in removing it as long as it continues to flow. Therefore, he is required to perform istinja' (ablution after relieving oneself) and bind the affected area with something that prevents the impurity from spreading to his body and clothes.

As for situations other than prayer, he is required to perform istinja' and bind the affected area, wash whatever part of his body has been touched by the impurity, and wash his hands if he touches the impurity.

The treatment for obsessive doubts (وساوس) is to disregard them, not to yield to them, and to turn to Allah with supplication (دعاء). It is also advisable to consult a specialized doctor regarding the incontinence.