Back to the doctor for you. This is a mycoplasma infection which can take a bit to kill it. Use a condom with your wife for now as you can actually pass it sexually. The reproductive tract of both men and women usually have bacteria in it but it is balanced and it is fine. When it gets unbalanced, you have situations like yours and this can include itching and pain. This type of bacteria when overgrown needs to be treated with antibiotics. You've taken the first line of treatment but there are drugs to go to if those don't work. Go back to your doctor. Here's a helpful article https://www.medicalnewstoday.com/articles/321636#diagnosis to add along to the other one given above.
Here is a link. Scroll down until you get to ureaplasma parvum.
https://www.webmd.com/a-to-z-guides/mycoplasma-infections#3
Because you still feel pain in your urethra, contact your doctor again and possibly take one more round of antibiotics. If your wife were pregnant now, there would be precautions to take for the baby's sake, but it is not uncommon to find ureaplasma parvum in a healthy woman's cervix or vagina, and for it not to cause any problems. Meaning, if she is not pregnant, I would not be too worried. If you two are trying to get pregnant, ask your doctor if your wife should also see her doc to get tested and possibly a run of antibiotics.
And no, infections of the urethra don't cause the sperm count to drop.