You will not pass this infection on to your wife, its not that kind of an infection.
I would do as suggested by your Doc. but also this could be related to kidney stones and or appendix issues if it is on your right side?....Try also follow dietary advice on easing a grumbling appendix and if you have small kidney stones. Watch for fungal overgrowth in the gut after antibiotics as they also affect the good bacteria and can cause a series of issues that can go unchecked. Simple dietary changes can help. Particularly less salt and no sugar and having full fat yogurt of natural type to help restore the good bacteria. Also power green juice smoothies can also help. These are a good detox for anyone in good health also. I hope your pain resolves as it could be many things.. I was diagnosed with 3 different things including all of the above but it turned out to be a grumbling appendix. And fungal issues caused by antibiotics in the past.. I hope this helps but don't worry if the pain doesn't go .. It will resolve but I would suggest to ask your doc for an ultra sound scan. ..and look up green juices and cut down on alcohol grains fatty foods and coffee for a while.this will help to cleanse your gut incase that is affecting your right side and right testicle.....most of above I have also experienced myself and happy to give more advice on diet.
I just thought that because my dr said it wasn't std related that I might not be able to pass it to her
It seems obvious that you may infect her with bacterial epididymis.