As you have had these lumps for 3 years now, I don’t think you should be worried too much. A malignant lump in the male breast is relatively rare especially since these lumps are movable, don’t seem to have grown and you don’t have nipple discharge or noticed any skin changes.
Nevertheless, since these lumps are still present, it is necessary that some type of testing be done if you want to know exactly what’s going on. Yes, a Mammography can be done and it’s often more accurate in men than in women, because males do not have dense breasts or other common breast changes that might interfere with the test. Also an Ultrasound can be very useful to see if a breast lump or mass is a cyst (fluid filled sac) or a solid tumor.
If your doctor does not order these tests, and you are obviously worried about these lumps, I would advise you to consult a Breast Specialist who will examine you and let you know if further investigation will be needed or not.
Take care and I hope this helps.
Men can have mammograms, but it's unlikely that you have breast cancer. On the other hand, it's better to be safe than sorry. Maybe you should have one or both lumps removed and examined under the microscope.