I work in an Orthopedics office, I would say have it checked out. The X-rays and things of that sort is frustrating but actually necessary. X-rays allow us to see a bit more than just broken bones. You can see narrowing of the joint space (osteoarthritis), bone spurs, or misalignment that may be caused by partial or full rotator cuff tears (which would then indicate the need for an MRI to evaluate just how large of a tear, and if it would be surgical, etc.). What happens is that the doctors are required to treat conservatively first, because that is the only way things are approved and paid for (at least in part) by insurance. Insurance requires them to say they tried conservative treatment before they can try anything further, unless it is something glaringly obvious upon X-ray and physical exam.
Speaking from what we do at our office, typically, we would start by getting X-rays, and then examine you - but from what your saying we would probably be looking at starting off with NSAIDs and Physical Therapy.
You don't have any crazy deficits in range of motion with that shoulder or extreme weakness in it, correct? Typically that would be evidence of something more acute, and you probably would've noticed a specific moment of injury. The popping and clicking sounds more like the tendon sheath encountering some resistance somewhere as it moves across bone, which could indicate tendonitis. At worst, there is possibility that something like that could eventually lead to some sort of tear, but we can usually prevent that by getting the inflammation down.
I'm by no means a doctor, but I often scribe for our orthopedic surgeon here so I learn quite a bit by listening to what he advises with his patients and observing the various special tests he will use to determine what is going on in the patient. Basically, I'm saying don't take my word for it but get an expert to look at it.