First, you don't say how the NGU was diagnosed. According to the history you give, I would wonder whether the diagnosis is accurate. The symptoms you describe are not typical, so if the STD clinic provider did not actually document an abnormal urethral discharge and/or inflammation (white blood cells) in your urethra, the diagnosis may be in question. And you are exactly right that NGU symptoms don't show up in 2 days; it always takes at least 5 days and usually 7-14 days. On the other hand, most STD clinics' diagnoses of NGU probably are reliable. But even if you had NGU, some cases are relapses of past infections, so you didn't necessarily catch it recently.
But the rest of my responses assume you indeed have a new case of true NGU.
You cannot catch NGU through a condom or by a hand job. So it seems sex with your wife is the only possibility. Some cases of NGU are due to respiratory viruses that can also infect the genital tract, in particular some strains of adenovirus. And adenovirus often causes conjunctivitis, so that sort of fits. Other cases of NGU are due to normal oral bacteria, so if your wife performed fellatio on you, that's a possible source. Note that neither of these possibilities has any implication about your wife having other sex partners.
Bottom line 1: Confirm that a definite diagnosis of NGU was made. If not, your symptoms are equally compatible with chemical irritation (e.g., from lubricant, especially if the condoms contained spermicide) or with something else nonsexually transmitted.
Bottom line 2: Just complete your antibiotic treatment as prescribed, then follow up with the STD clinic if you remain concerned.
Bottom line 3: Your wife should be treated if that hasn't yet been done. It's a good bet she doesn't really need it, but that is standard practice, and better safe than sorry.
Good luck-- HHH, MD
My wife hasn't performed fellatio in about 5-6 months.
I know anything is possible but I 100% believe my wife has not had sex outside of marraige.
Thanks for your help