
Joe, I have already give you my thoughts on this.
You must exclude any body cleansers from getting onto the skin of your penis - and yes I know this is difficult if you shower, but you need to spend sometime at the end of the shower rinsing your penis with the running water, after you have washed everywhere else and rinsed thoroughly.
So yes, your penile skin is irritated, the only way to stop the irritation is quite literally stop anything that is a potential irritant from getting onto the skin of your penis, otherwise, simply, this will continue as it is …
urologist here
you should never use soap on your penis as it’s the same material in your eyelids- imagine if you got that soap in your eyes, that’s what it’s doing to your penis
for the time being use some jock itch cream or anti itch cream