The swollen glands suggest an infection, but it is a non-specific in that it can occur from any type of infection.
If there is mild discomfort of the penis and no discharge, there are a couple of infections that are common. One is a sexually transmitted germ, called chlamydia, which is one of the more common sexually transmitted disease. Gonorrhea can also cause irritation of the penis, but would usually cause more significant discomfort or pain and have a discharge, so would be unlikely in this case. There is a test that can be done on a penile swab for either gonorrhea or chlamydia, or both, so your doctor may have checked for these germs.
The other common infection is non-gonococcal urethritis, or NGU. Actually, before we had good tests for chlamydia, a chlamydia infection was also included in the diagnosis of NGU. At the time, we could only effectively exclude gonorrhea, so all remaining germs were lumped together. Now that we can exclude both gonorrhea and chlamydia, there are still some germs that are not sexually transmitted that can cause NGU, including Ureaplasma urealyticum, Mycoplasma genitlaium, and Haemophilus vaginalis. Identifying these germs is still difficult, so we usually will treat empirically once gonorrhea and chlamydia are excluded. There are a couple of antibiotics that are effective against NGU, including the Zithromax, but it is also common to use doxycycline. In your case, sicne the Zithromax has not helped, it would be common to try a course of doxycycline.
If I can provide any additional information, please let me know.