Is it correct to observe a 15-day purity period, especially with the intermittent discharge of yellow or brownish fluid before the completion of this period?

The brownish discharge that caused the obsessive thoughts is not considered menses unless it is connected to blood or occurs during the usual period. There is no issue with these discharges, and there is no need to consider the matter of the minimum period of purity (tuhur). It is permissible for the person suffering from obsessive thoughts to adopt the view of the majority of scholars if it is easier for them, because they are allowed to follow the most lenient opinions until Allah cures them of the obsessive thoughts.