Hello,
From your symptoms the possibility of intertrigo is high. For the penile symptoms, fungal infection and eczema skin need to be ruled out. An intertrigo is an inflammation (rash) of the body folds. It most commonly occurs due to bacterial, viral or fungal infection. An intertrigo usually appears red and raw-looking, and may also itch, ooze, and be sore.
Please get it examined as nothing can be confirmed without examination. It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
You could have contact dermatitis. Anything from lubes, clothes detergents including fabric softeners, lotions, soaps, and cologne can cause it. My husband has bad reactions from Purex detergent and he has the same issue that happens just like that. A secondary infection like MRSA can happen if the rash isn't properly taken care of as soon as it appears.
Try to think if there has been any changes in anything that can touch down there, including your cup if you play sports. If you have used something once before without an allergic reaction and used it a second time and developed a rash you could have sensitized your skin to whatever product was used and then broke out after the second go around. As for right now, use baby shampoo and/or baby soap to cleanse the area since it is a sensitive area and baby products are very mild. You can even use hypoallergenic baby products too. The less product build up and the less aggressive cleansers the better, right now. Also, if you are sexually active ask you're girlfriend/partner if she has changed anything that could be touching your area.
As far as the dry part, try some hypoallergenic lotion. So many lotions, even baby lotion, have fragrance added and it can cause the rash to spread or even become very painful. I would try just some Vitamin E gel. It's not a cream, lotion, or anything that will cause the skin to be smothered. I found some at a dollar store and it's Fruit of the Earth Vitamin E Gel. It wouldn't smother the rash, but it would moisturize it.
Personal Experience: I color my hair quite often. I used black hair color to color the underneath part once and I didn't break out. I did a touch up with the same product and I broke out severely. I had a rash on my scalp, just where I put the product, for many weeks. I would use my normal shampoo and it made the rash worse so I decided to try baby shampoo until the rash subsided. It helped so much.