I'd have to go with balanitis, too, if everything else is negative.
Think of everything. You mention allergies - perhaps you are having a sensitivity to a soap or detergent you are using. Even if you haven't changed any products, allergies can develop at any time. Perhaps one of your products changed it's formula - think "new and improved".
You mention sex makes it worse - are you using condoms with a lubricant or spermicide? Have you changed lube, if you use it? Here are some natural ones that may help, though some are designed for women -
https://www.menshealth.com/sex-women/a19536336/pick-the-perfect-lube/ - this is VERY hetero, but has some good info on why both men and women can react to different kinds of lube.
http://bestlubezone.net/best-lube-for-sensitive-skin/ - not so hetero, some decent recs
There are a ton of other sites out there if you're interested. I started searching "lube for sensitive skin", then added "lube for sensitive skin men", then added "gay men", etc. (I don't know if you're gay, bi, pan, whatever and that's not at all my business - I was just trying to get some results that weren't all designed for women.) It's quite the rabbit hole once you get started lol.
When you notice the wetness, gently dry the area. Keep it clean. If it's possible your weight is causing an issue, start working on that. I know with medical issues it isn't easy, but start slowly.