A sore developing after a day wouldn't be from any STD - that's too soon.
Since you are responding to the moisturizer, I'd guess it's really dry skin, or eczema or something along those lines. After we get through the covid stuff, you might want to see your doctor about this, but I don't think this is an STD. Your doctor may have a cream that helps resolve this more than your normal cream does. It could also be a fungal infection from the antibiotic, which is quite common.
Your herpes test at 13.5 weeks is conclusive. It's not herpes.
If it continues to bother you, or gets worse, see your doc or a dermatologist, but you can rest assured it's not an STD.
Just to add a couple of things. The sore on my inner thigh was over a hair follicle and I was wearing tight jeans, so I'm wondering if it was just an irritated hair follicle. I had a dermatologist who looked at my groin a week before and said I had eczema. A couple of weeks after I went to my GP who looked at my glans and groin and said nothing looked untoward and agreed with the derm about eczema in my groin folds. No blisters have occurred on the base of my penis. The only thing that has got me worried is that I fingered her and touched my penis 10-15 mins after. The timing of these symptoms has got me worried and the recurrence of this sore red skin in my groin. If anyone can give me some reassurance that would be great.