The desire to be physically or mentally ill is a characteristic of factitious disorders. Please keep in mind that I cannot know with certainty if you have a factitious disorder. The only symptom you have described is your strong desire to have a mental illness. It is an unusual symptom but an accurate mental health diagnosis could only be made after a thorough mental health evaluation.
In the category of factitious disorders are mental health conditions in which an individual pretends as though he or she has a physical or mental illness. Individuals with these disorders seem to have a strong desire to be seen as injured or ill. They deliberately create a set of symptoms for the purpose of gaining attention and sympathy from others. Individuals with factitious disorders might create symptoms that do not exist or lie about their experiences. They may also seek out diagnoses or insist that they have an illness. Some individuals with factitious disorders eagerly undergo risky or painful medical testing and procedures.
I suspect that the real need you are attempting to fulfill is a desire for attention. Generally speaking, that is the primary reason why individuals pretend to have an illness. They want people to notice them. Individuals in society have sympathy for those with a physical or mental health condition (though less so for a mental health condition). Perhaps you think that if you had a mental illness, your family and friends would have to pay more attention to you. You may believe that having a mental illness would ensure that you are the focus of their world. It is, after all, difficult to ignore a “sick” person.
I suspect that your desire to have a mental illness is a misguided attempt to gain attention and sympathy. It is human nature to need and to want attention but pretending to have a mental illness is not a healthy or appropriate way to gain attention.
If you are willing, you should speak to your parents about seeing a therapist. A therapist can teach you alternative and healthier ways to meet your emotional needs, that do not involve lies and deception. The “find help” tab at top of this page can help you and your parents locate a therapist in your community. Please take care.