that doesn't sound like an std. And it's way later from when you had the sexual exposure. I'd look more to it being a skin issue. We can get dermatitis on our penises. You do have symptoms of jock itch on your penis. They are: redness
persistent itching
burning sensation
flaking, peeling, or cracking skin
rash that gets worse with exercise or activity
changes in skin color
rash that doesn’t improve or worsens, or spreads with over-the-counter hydrocortisone (anti-itch) cream
Just to list them. The flaking and peeling may be what you are saying is dryness.
You are applying otc products. Which sometimes will work. But since it hasn't, any chance you can get to the doctor to take a look? You may need a different topical agent to clear this up.And if it is dermatitis OR ezcema, it would be a different situation entirely. https://www.healthline.com/health/jock-itch#treatment and https://www.webmd.com/skin-problems-and-treatments/eczema/what-to-know-about-eczema-on-the-penis
I think you should go see your doctor to get to the bottom of this. But take STD out of your mind. This is a dermatology problem from what you've described.
Don't know what you have, but dryness is different than jock itch. Jock itch, which I've had, is a fungus called ringworm, and it usually shows as a light red ring at the edge of your pubic hair. It could be in other places, but that's where it has shown up when I've had it. It does often come back if you use antifungal meds, as they also harm the beneficial organisms that protect us from such things. The eggs are also not usually killed off, and so it often takes more than one application period to kill it off. But if you've seen a doc, one would hope the doc told you what it was and didn't just give you an antibiotic in order to get rid of you, as they often do. So did he say it was ringworm? Did he say it might be an STD, which I doubt it is? Did you ask for a test? You can't treat very well what you don't have a diagnosis for, and if it's just dry skin, as you mention you have, that can cause itching as well.