Hi again, the red rash is most likely just an inflamation as no std shows symptoms of a red rash. You mention a discharge in the morning. If its clear sticky its almost certainly natural mucus that is being forced out your penis from milking. But its its white (bright white/gray) that would indicate an infection. Taking antibiotics kill both good and bad bacteria and could actually cause a UTI but thats really not common.
If you have a white discharge and tested negative for gono and chlamydia your only left with a UTI also called NSU which is a non specific urethra infection.
I really suspect your anxiety is adding fuel to your symptoms.
A red rash can be a lot of different things, e.g. balanitis and lichen plantus, and of course yeast as well. Anyway, doxycycline and azithromycin AND rocephin (ceftriaxone) covers basically all the STDs you can name, from syphilis to gonorrhea to chlamydia to even chancroids (H. ducreyi). Of course, it doesn't cover the viral ones like HIV and HSV, but then neither of these cause discharge.
Moreover, I don't think the discharge has anything to do with STDs. The only STD that has an incubation of less than one day is reinfection of scabies, as I recall it. It might be a yeast infection if anything, which the antibiotics you took definitely would have taken care of.
And I agree with Dave. Your anxiety could've caused many of these symptoms.