Since these symptoms have persisted for a while and are not responding to your initial efforts to clear them up, I would recommend going to see your primary care doctor
, who will be able to establish a diagnosis and help you decide what treatments to pursue.
I can think of several potential causes of your symptoms. One of these would be a yeast infection, which typically causes red dots that spread outwards over the skin, similar to those which you are experiencing. They tend to be uncomfortable or itchy, but not always.
Another potential cause would be herpes, which is a sexually transmitted infection. In the initial stages, herpes causes small blisters or ulcers that are very reddened at their base. One thing that argues against herpes in your case is that herpes does tend to be quite uncomfortable, but I think it still does need to be ruled out.
Finally, you could have a condition called balanitis, which is an inflammation/infection of the skin of the tip of the penis, most common in men who are uncircumcised. Usually balanitis will respond to simple measures like increased washing, as you have been doing, but sometimes an antibiotic ointment is required. Please speak with your primary care doctor.