You have a legitimate question. After 3-4 years of treatment, I don’t think you are impatient. What you didn’t share with me is whether you have talked to your therapist about how helpful it would be to have a diagnosis. My guess is that he/she has a working idea of what is going on with you. It may be that you have a number of overlapping issues and, since you are so young, she’s reluctant to come to a decisive conclusion. But that’s a discussion worth having.
Do bear in mind that diagnoses are not facts. They are helpful in giving professionals a direction for treatment. They are helpful for professionals to use for talking/conferring with each other. But they aren’t intended to label a person. They aren’t intended to settle once and for all who you are.
But you’re correct. They can help a person feel more comfortable and they can open up other avenues for conversations and treatment (like a support group or group therapy, for examples).
I urge you to have a frank discussion with your therapist. You started seeing her when you were only about 12. She may have withheld a diagnosis at the time because you were too young to understand its implications. But you are 16 now and old enough to become more of a partner in your treatment. Talking about her thoughts about diagnosis and your reaction to it may shift your therapy in a positive way.
I wish you well.