Welcome to ASHA's Ask the Expert forum. Thanks for your question.
You present a very interesting case!. I'm happy to help. Please clarify one aspect: you consistently write that you diagnosed and treated yourself, but unless you are a health professional with easy access to clinical services and labs, most of this would normally be undertaken by a physician. Are you under professional care or entirely on your own? Whether it's you or someone else, your management has been almost textbook perfect for the various STDs that could cause this problem -- somewhat overtreated, but with obvious attempt to correctly cover gonorrhea, chlamydia, NGU, herpes, and even non-STD UTI.
But I believe I know exactly what is going on: I believe you are correct in speculating about adenovirus. Indeed, I could copy your question and use it as an ideal case to teach med students and residents about adenoviral urethritis. Adenovirus is primarily a respiratory pathogen, but some strains readily infect the urethra. Typically adenovirus urethritis symptos are dominated by urethral pain and dysuria (painful urination) with scant or no discharge. Onset 3-4 days after an oral sex exposure is typical; infection typically comes from a partner's oral cavity. And most dramatically in your case, simultaneous conjunctivitis is very common, and your other upper respiratory symptoms also are consistent. Finally, it sounds like your urethritis symptoms are improving gradually, more or less on schedule. I expect they will be entirely gone in a few more days. There are no reported long term complications.
So at this point I strongly recommend you stop all treatment and cease any additional diagnostic tests. For sure don't treat or test for M genitalium, which is not known to infect the oral cavity or be acquired by oral sex (and your symptoms aren't typical for it). Steroids probably wouldn't hurt at this stage, but there are no data and I don't think they would help; better to just let it clear up on its own.
Here is a link to a recent report reviewing NGU due to adenovirus. Several others also have been published in the past 20 years. http://www.ncbi.nlm.nih.gov/pubmed/26574571
I hope this has been helpful. Best wishes and happy new year--