What should a woman do if semen, discharge, or prostatic fluid is released without arousal, and it is difficult to distinguish between them, especially noting the occasional release of a thick yellow fluid? Is it permissible for her to touch her private parts or insert her finger to ensure no fluid is present?

The cure for obsessive thoughts is to ignore them and not pay attention to them. If the discharge is a normal yellowish color, it is obligatory to perform istinja' (washing the private parts) and wudu' for prayer, and it is not considered menstruation. Ghusl (ritual bath) is not obligatory unless the discharge of semen, which necessitates ghusl, is confirmed. If you doubt the nature of the discharge, you have a choice to assign it the ruling you prefer. It is not prescribed to insert a finger into the vagina or to search for discharge. Rather, it is obligatory to pour water over the impurity until it is highly probable that the impurity has been removed.