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This could be caused by a couple of things. Given your symptoms and the duration of the bumps, they are most likely either a benign viral growth, or a type of normal skin variant.
It's possible that these are caused by a viral STD, or human papilloma virus (also known as genital warts). There are about 80 different strains of HPV, and 80% of the adult population will contract some form of it sometime in their lives, so it's very common. Condoms aren't even all that effective in preventing transmission of this virus. The same strain may cause warts or symptoms in one person, but not another, and the appearance of these growths vary wildly. They can be pink, flesh colored, white, or tan, very small (even nearly invisible) to very large. They are not fluid filled, and not "popable" (though they might bleed or be tender if you pick at them). If left alone, they shouldn't hurt, but some do cause itching in some people. In many cases, the warts will go away on their own without treatment after a period of months. There usually isn't any medically necessary reason to remove them if they're not causing any problems, but there are topical medications, and oral medications that can help get rid of them, as well as burning, freezing, laser surgery, and surgical excision. The virus remains in the body for life, so they might recur, even after removed. Syphillis and herpes both cause bumps as well, but more typically result in draining ulcers or lesions. Fungal infections and irritation are possibilities for penile bumps as well, but your particular description of symptoms indicates that neither of these is likely. Another viral possibility is a type of papule caused by a virus called molluscum contagiosum. They can vary in size or color, but are contagious, such as HPV.
You can find a picture of it on a penile shaft here (warning: graphic image): http://www.atlasdermatologico.com.br/listar.asp?acao=mostrar&arquivo=Molluscum_Contagiosum14.JPG
There are also a few normal variants that cause bumps and are not a cause for concern either. One condition is known as "pearly penile papules," and consists of whitish, pink, or flesh-color bumps that appear only on the head of the penis or along the glans (rim), and aren't itchy or painful. Anywhere from 8-48% of men have this, with more of them being uncircumsized (though it occurs in circumsized men as well).
You can read more about it here: http://www.emedicine.com/derm/topic313.htm. Another perfectly common condition is raised sebaceous glands on the head of the penis, and it can present itself as small raised bumps. This is also a normal variant and wouldn't require treatment.
Unless they are bothering you (itching, pain, draining, or grow large), the only reason you would have to seek treatment is if you preferred removal for cosmetic or transmission reasons. Viral growths are contagious, and you can spread them to other areas of the skin, or to a sexual part. Having them removed does not remove all chances of spreading it, but it has been shown to help. Normal variant bumps, of course, are not contagious, but can still be cosmetically altered if you desire such. A blood test or biopsy could be used to determine, exactly, what these are. You should try to avoid picking or squeezing them; if they are viral, this activity can cause them to worsen or spread.
I hope this helps! Let me know if you have any further questions!
For normal variations (penile papules, raised sebaceous glands), there are no medications specific for treating this, though "cosmetic" laser surgery might reduce the appearance.
For viral growths, there are no over-the-counter medications, and a prescription must be obtained from your doctor. There are some topical ointments you can apply yourself at home including: imiquimod (aldara), and podofilox lotion or gel (condylox). While effective, these may take a little longer than other treatments to work. Other topical agents are harsher and quicker, but your doctor will need to apply these in his office. These include any of the below (click on links to read more; from http://www.webmd.com/sexual-conditions/HPV-Genital-Warts/guide/Genital-Warts-Human-Papillomavirus-Medications):
I've heard of oral antiviral medications, such as Valtrex (normally used for Herpes), being used to try to push HPV into remission. Of all treatments, this is probably the least effective. Interferon alfa is another medication that injected every day for 3 weeks, or a similar schedule and duration. There's also surgical removal through cryosurgery, electrical cautery, laser surgery, and excision, which is highly effective, but more painful and expensive. You can read more about treatments/side effects/and success rates on this chart: http://patients.uptodate.com/image.asp?file=gyne_pix/treatm81.htm