Hello,
It is better to get KOH examination of the skin scrapings to confirm whether it is a fungal infection. A biopsy skin can also be done to rule out eczema and atopic dermatitis. There are certain other non-pharmacological measures which are equally important in treating atopic dermatitis. These are avoiding harsh soaps and cleansers, preventing scratching or rubbing whenever possible, protecting skin from excessive moisture, irritants, and rough clothing, maintaining a cool, stable temperature and consistent humidity levels, limiting exposure to dust, cigarette smoke, pollens, and animal dander & Recognizing and limiting emotional stress.
Apart from that please get an evaluation done from a dermatologist to confirm the diagnosis as treatment is specific for each.
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.
I don't know about eczema on a penis as I am a girl but I do have recurring eczema on my fingers that can get really bad and I can tell you some of the things I do for that. Eczema and moisture don't get along so try and keep yourself as dry as possible. Also with mine my doctor had told me to apply cream before bed and then wear a glove overy hand while I slept to allow cream to do it's work without just evaporating off. I'm sure maybe you can rig something up to do that, and it may help. Also vitamen e is very good for your skin, i I I either take the capsules or puncture the oil ones and apply it directly to the skin. Also aloe Vera, the actual plant where you break off a stem an use the inside on the skin.
You are very lucky it is not bothering you as much as eczema can. I'm not sure how much this will help with that body part but just be glad it isn't an STD. And remembering this is just advice, I am not a doctor.