There is nothing embarrassing about talking about your breasts.  The only embarrassing thing is to find out that you have breast cancer, and that you could have avoided it with breast self exams and more open discussion.

Where do you begin with this topic?  With a breast self exam.  These should be done frequently and thoroughly and there are many ways you can learn more.  YouTube actually has a number of videos about doing self exams.  Your doctor can certainly show you how to do them as well.
You should also have a mammogram done.

At certain ages, they recommend that they be done once a year or more often, depending on your family history.  Speak to your doctor to see if you need to have one done now.  A mammogram is a breast exam that captures on X-ray image of your breast and looks for lumps, cysts, calcifications and more.

Make sure to get the information that you need so that you can keep yourself safe and healthy.