So first, forgive me. I am old and uncool, and don't understand young people language, but I will do my best. If I miss something, let me know.
So you had unprotected sex over a year ago, tested positive for gonorrhea, and got treated. Do you remember what medicines you got for that? Did you get a shot?
Assuming you got treated properly for that, and you've had no other sex partners than what you describe, you don't need any other testing. It sounds like your doctor is correct with the diagnosis, especially since your symptoms responded to the treatment.
If you've never had an HIV test, you should get one, but I wouldn't worry overly much about that.