Welcome to the STD forum. I'll try to help.
It can be difficult for a distant expert to judge the diagnosis of a patient's own health care provider. However, I am skeptical that you have NGU or that you ever had it. Your symptoms are not typical. By far the most common symptoms of NGU is abnormal discharge from the penis; although urinary discomfort or pain can accompany it, most men with only that symptom usually are not found to have urethritis. "Some WBCs" in urine doesn't mean much by itself; a few WBCs can be found in most urine specimens, and the negative LE test indicates the numbers were small and probably not significant.
Having said that, the improved symptoms with doxycycline is suggestive. Doxy can initially help NGU, followed by relapse of symptoms -- but in general that relapse occurs 1-3 weeks later, not 3 days. And doxy has anti-inflammatory characteristics, so it might have just helped control the symptoms without having any effect on the cause.
The standard recommendation for NGU that fails to respond, or relapses, after doxycycline is to treat with a macrolide antibiotic plus a treatment for trichomonas, i.e. metronidazole (Flagyl) or tinidazole (Tindamax). If you cannot tolerate azithromycin in the usual 1 gram single dose, you could take 250-500 mg once daily for 3-4 days. At that dose I doubt it will cause any side effects. If you still can't tolerate it, discuss erythromycin or clarithromycin (trade name Biaxin) with your doctor.
As for herpes, it also is not a common cause of symptoms like you describe. If there are symptoms at all from new genital herpes, the typical blisters/sores are usually present.
But you should expect that no specific cause is going to turn up, and over time, the symptoms probably will gradually resolve. There is really nothing to worry about in terms of serious health impact. I have never heard of problems like this leading to anything important (no cancer, infertility, etc) or to cause any health problem in patients' sex partners.
Here are a few other threads that discuss various aspects of NGU that you might find interesting.
http://www.medhelp.org/posts/show/757304
http://www.medhelp.org/posts/show/757304
http://www.medhelp.org/posts/show/774818
http://www.medhelp.org/posts/show/1228688
Regards-- HHH, MD