Hello Sir,
Yes, this is possible, and quite frequent especially during temperature/season changes.
For such sensitive skin, it is suggested to apply a moisturizer without perfume like Aveeno, Glaxal Base, Cerave or other, 1 to 2 times a day, or more if desired or if itching.
It is also suggested to use a fragrance-free soap such as Dove, to avoid water that is too hot or too cold, and to avoid rubbing too vigorously after a shower or bath. Instead, lightly pat and apply moisturizer quickly after getting out of the shower/bath.
I encourage you to try these measures, on the skin of the penis as with other parts of the body, and to be persistent with the application of the moisturizer.
I hope I've been helpful, and I'm available if you have any further questions!
Tom Samaha, pharmacist