When test results become (or remain) negative on antibiotics, it is because cure has occurred or no infection was present to start with. You probably never had an STD in the normal sense. If you did, you can be sure it is gone now, as I said in so many words (last paragraph of my reply).
If there is no observable discharge of pus or mucus and no elevated WBCs in the urethra, then there is no NGU.
It is unlikely that you need antibiotics at this point or that continued antbiotic treatment of any kind will be helpful. As I said above, if this started out as NGU (which in my opinion is by no means certain), that problem has long since gone and I doubt you have any persisting infection. That doesn't mean you don't have symptoms; clearly things are not right. But the residual problem sounds more like a mechanical obstruction or a non-infectious inflammatory problem.
Further questions really need to go to your urologist. We are beyond the expertise of an STD specialist.
Welcome to the STD forum.
Most likely you indeed had NGU when this all started, especially if the doc who diagnosed it is reasonably up to date on STDs. Oral sex is a plausible cause, although NGU following oral sex often is not due to the garden-variety STDs. For example, it is almost never due to chlamydia, which is rarely infects peoples oral cavities and therefore is rarely transmitted by oral-genita contact. (That is, your urologist is wrong on that score. But don't blame him too much: it may seem surprising, but many urologists receive little or no training in STD and infrequently are called upon for STD diagnosis and treatment.) Some orally acquired NGU cases may be due to entirely normal oral bacteria. Others are caused by respiratory tract viruses, especially some types of adenovirus.
Azithromycin is the drug of choice for NGU. Ciprofloxacin usually is not recommended but didn't hurt anything. Doxycycline is the recommended treatment when azithromycin fails. Accordingly, you have been treated as well as anybody could expect, as you already seem to know. The only caveat is that there has been no research on the best treatment for orally acquired NGU.
Now to the current symptoms: Neither NGU nor any other STD causes the problems with urine flow that you describe. It sounds to me like partial obstruction of the lower urinary tract, of the sort that might happen from a prostate gland problem or urethral stricture. Whether or not sexually acquired NGU was indeed the correct initial diagnosis, this has morphed into something else. This is an area outside my expertise, but it is bread and butter for a urologist. Accordingly, I suggest you continue to work with your urolofist. I doubt you have any continuing infection of any kind -- although many urologists prescribe antibiotics in the hope they might clear things up.
Sorry I can't be more helpful. Good luck with it-- HHH, MD
Thanks for your responses. Just a couple quick follow-ups, if you'll humor me.
When I retested 12 days after finishing the cipro, or 19 days after taking the azithromycin, would those test results be conclusive or would they still be contaminated by the antibiotics I took?
If I want to be absolutely sure that I have no STD at this point, would a WBC count of a urine sample or urethra swab be useful? Should I do something else instead? How long must I wait after I stop taking the doxycycline for any new test to be informative?
Thanks again.