It is conceivable your symptoms reflected undiagnosed NGU. However, most NGU has discharge as a more prominent symptom than just "slight burning". False negative results for either gonorrhea or chlamydia are rare with NAAT; and in any case, even without treatment, virtually all cases of urethral gonorrrhea and the large majority of chlamydial infections clear up on their own within 6 months.
So all things considered, I see no reason for concern that you continue to harbor NGU or any other STD at this time. But of course if in doubt, don't try to figure it out online; see an STD-knowledgeable health care provider, such as your local health department STD clinic. But truly I see no reason for concern here.
Best wishes-- HHH, MD