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You seems to have a condition called Balanitis, due to candida. The dryness and cracking on the penis is due to this candidal infection ( a kind of fungi). It can be a STD also if you are sexually active.
The diagnosis can be confirmed by a KOH smear.
You can apply a antifungal cream like 1% clotrimazole twice a day for a week. (OTC - Lotrimin) Keep the penis and surrounding area dry.
Hope this helps
Patient replied :
I have purchased both Neosporin and Lotrimin. I was told to use Neosporin in order to keep infection away. Can I use both at the same time, or just the Lotrimin? How long will it take for the cracks to go away?
Use only lotrimin. It might take 7 days approximately. However please note the best approach will be to get tested to be 100% sure that this is candidal infection. Thank you