It is conceivable you acquried NGU, and the timing certainly is consistent with that possibility. However, the symptoms you describe are not typical for NGU or any other STD. NGU symptoms are identical to those of chlamydia, which you have experienced.
So prostatitis indeed sounds like a good bet -- or, perhaps more likely, the chronic pelvic pain syndrome. If you google that term, you'll find lots of information that might sound familiar; start your reading with the excellent Wikipedia article, which is one of the top google hits. As you will see, CPPS used to be considered a form of non-infectious prostatitis, and some urologists and other providers still would call it nonbacterial prostatits. However, you will also learn that the prostate gland might not be involved at all as the source of pain.
Ciprofloxacin may or may not have any effect. CPPS, and many cases of true prostatitis are not due to infection at all, and antibiotics don't help. If indeed you actually had NGU, ciprofloxacin probably would clear it up. Cipro hasn't been studied extensively for nonchlamydial NGU, but probably is effective.
Having said all that, there is the issue of onset of symptoms 4 days after a new sexual exposure, so I cannot say for sure you didn't pick up an infection. Prostatitis and CPPS are not sexually acquired (except to the extent that CPPS often has an emotional component, which could be related to anxiety from the sexual indiscretion). But if your symptoms clear up and you don't have sex with your girlfriend until you finish the cipro, she should be safe.
I hope this helps. Best wishes-- HHH, MD
And yes, reduced force of urine stream suggests a prostate problem, which can go along with either CPPS or true prostatitis. And at 40, you're right at the age when prostate symptoms become common. Presumably you told your doc about that symptom. If not, do so at your next appointment.