You don't describe the timing, i.e. the interval from performing fellatio and onset of your symptoms. Assuming only a few days or less, it is highly likely you acquired an adenovirus infection. Adenoviruses most commonly cause upper respiratory infection; they are frequent causes of common colds. Many strains have a predilection for conjunctivitis (pink eye) in addition to pharyngitis (throat/tonsil infection). Bronchitis or pneumonia are fairly common as well, and would fit with your cough.

Like other viral upper respiratory infections (URI), adenoviruses are spread primarily through non-intimate contact with respiratory secretions or by kissing, but over the past couple of decades several studies have shown them to occasionally infect the urethra by oral sex, with resulting nongonococcal urethritis (NGU). But obviously they can be transmitted in the other direction as well, i.e. penis to oral. Or if you also kissed your partner, perhaps that was the source rather than performing fellatio. STI experts and infectious diseases physicians have come to understand all this, but many other health care providers are unaware of genital adenovirus and the role of sex in transmitting some infections. So it isn't surprising that your optometrist didn't think of this possibility. 

In case you're interested in learning more, here are two medical literature citations, one reporting that adenoviruses explained around 5% of NGU cases in Melbourne, Australia and the other an editorial I wrote to accompany that article. You can find more if you google "adenovirus" and either "urethritis" or "sexual transmission".

https://pubmed.ncbi.nlm.nih.gov/16388479/

https://pubmed.ncbi.nlm.nih.gov/16388480/

You don't mention whether the urgent care clinic did a throat swab to check for oral gonorrhea. However, that was unlikely:  the large majority of oral gonorrhea cases are entirely asymptomatic; and when it does cause symptoms, they do not include nasal congestion or cough. Chlamydia also is not known to cause any of the symptoms you had. HPV infections are asymptomatic until and unless they cause warts or pre-cancerous growths (e.g. of the cervix), typically several months later. They have never been known to cause symptoms like yours. Given all the other negative tests, I am confident you have no other STI from your New Years Eve adventures!

Adenoviral infections are cleared entirely by the immune system, and I doubt you minor-sounding continuing symptoms are due to ongoing infection of any kind. You may be having some residual effect of the initial infection, but if so you can expect them to clear entirely as time passes.

I hope this information is helpful. Let me know if anything isn't clear.

HHH, MD