Welcome to the STD forum.
Non-STD causes of urethral discharge are uncommon, especially in younger men (under age 30-40). Almost certainly you had sexually transmitted urethritis, probably nongonococcal urethritis (NGU), possibly gonorrhea. In other words, your initial assumption was exactly right. A few percent of such cases are due to gonorrhea, but the rest are NGU. About 30-40% of NGU cases are due to chlamydia.
MedHelp moderators are asked to avoid criticizing patients' own doctors. If you live in an area where gonorrhea and chlamydia testing are not available (e.g., some developing countries), maybe testing wasn't available. But it also was a serious error to not examine you to confirm the abnormal discharge and take at least prelminary steps to learn the cause. For example, gonorrhea bacteria can easily be identified under the microscope. The treatment you received is fine for chlamydia and NGU, but not ideal for gonorrhea -- although it usually would work OK.
The causes of NGU in the 60-70% not due to chlamydia are generally unknown and testing shows no abnormal bacteria. (Some organisms called Mycoplasma genitalium and maybe Ureaplasma cause some cases, but no tests are available for these bacteria except in research laboratories.) Therefore, your partners' negative test results does not mean it's not an STD. It is, and both of them need to be treated with antibiotics to prevent future health problems and to prevent transmitting the infection to other sex partners, or back to you.
If your discharge clears up and doesn't return in the next couple of weeks, you can consider yourself cured; you don't need to be reexamined or retested if the symptoms are gone. Talk to your partners and don't have sex again with either one of them until they are treated. Finally, find another doctor in the event you have a future STD or suspicious about it. Yours either isn't up to speed on STDs or is just careless about them. Your local health department STD clinic would be a good choice.
For lots of additional information about similar cases, use the search link and enter NGU; you'll find over 800 threads that have discussed various aspects of it.
Nothing serious is likely to come of this, so don't lose a lot of sleep over it.
Best wishes-- HHH, MD