It can be difficult to be sure what a patient means when they give a description like this, which is not exact enough to be certain about.
However I think because you say that these spots are on your scrotum as well as your penis, that they are sebaceous cysts (or pilar cysts, or wens – same thing, different names). This is a common area to have them, and you are not alone, neither in having them, nor in being embarrassed.
I have known young men avoid intimate contact with their girlfriends because they are worried about what they will think. This is a shame, because they are quite harmless, if a little unsightly.
They are usually white or cream in colour when they occur in this area, and are smooth little domes that stick up above the skin. They can vary in size from quite tiny to the size of a large pea, or even bigger. They contain a cheesy-like substance, which is made of breakdown products of skin tissues including keratin and sebum (the stuff that makes your skin greasy). They are quite harmless and cannot be transmitted to anyone else. They rarely give any problems in this situation apart from embarrassment, although the larger ones can sometimes get infected.
But what can you do about them?
I really think you should overcome your embarrassment and show them to your doctor.
If you are registered with a lady doctor, I am sure you could if you wished go and see a male doctor in your practice if that bothers you.
You must not think the doctor will find this unusual. We have all seen hundreds of such cases, it is all in a day's work. I am sure he or she will be sympathetic.
The only satisfactory way to get rid of them, if that is what you want, is to have the larger ones removed. This is a simple procedure that can be done under local anaesthetic, and many doctors like myself do this in their own minor surgery clinic at the practice, so you do not need to go to hospital.
So do stop worrying, and think about getting your doctor to...