If I have non gonoccocal urethritis. But I am experiencing no pain or discomfort at all and The meatus is only swollen. Does that mean no infection?

Non-GC Urethritis. Well, the question is what was ur symptoms when u presented to the doctor who diagnosed you? Non-GC Urethritis means an infection of Urethra with an organism rather than GC like Chlamydia, Uroplasma, Mycoplasma, some virus and also Trichomona, did you receive treatment with Azithromycin and Doxycycline? If you did absence of symptoms might need response to treatment, otherwise non-GC Urethritis.
Consider other bacs. No it does not. other bacteria can cause urethritis. You could have Chlamydia causing the urethritis or it could be a bacteria from your GI tract.