Irritation can cause red dots on penis head. Wash the area with a mild cleanser with moisturizing properties like Cetaphil and wear cotton clothes. Then apply a good hypoallergenic moisturizer over the area and see if this improves. If the symptoms still persist then you can apply mild steroid after consulting your doctor.
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.