I have shoulder pain. I have not had an injury and it does not affect my everyday. It throbs lightly. Should I see my doctor?

Wouldn't hurt. Many musculoskeletal problems come down to exactly what you're saying: whether it is affecting your daily life. You can get it evaluated, knowing that your physician may want to get imaging (xray, mri) in addition to a physical exam. If the pain worsens or begins to limit your ability to do everyday tasks, definitely go get it looked at.
Wouldn't hurt. Many musculoskeletal problems come down to exactly what you're saying: whether it is affecting your daily life. You can get it evaluated, knowing that your physician may want to get imaging (xray, mri) in addition to a physical exam. If the pain worsens or begins to limit your ability to do everyday tasks, definitely go get it looked at.
Depends. Depends on how much it is bothering you. Sometimes imaging is necessary to figure out the problem. Musculoskeletal ultrasound is great new tool for physicians trained in it -- to see inside your shoulder while you're moving it right in the office. It can also help precisely guide an injection if that becomes necessary.
Yes. See a non-surgical sports medicine physician, who could obtain xrays and perform a clinical exam, to help determine the root of your pain.