An mri is magnetic resonance imaging. An xray motly sees bone, and can hint at collections of fluid (such as blood). Of course, excepting gross trauma this is probably not meaningful. Your doctor, not knowing you from adam, wanted to rule out fracture, tumor etc. A ct scan just takes multiple xrays, so it really also sees bone and blood, but 3d. Not very helpful. MRIs look at soft tissue: ligaments, etc. Your rotator cuff, in simplest terms, is a stabilizing cuff of muscle and ligament in a circle around your shoulder. If a ligament or muscle attachment is torn, MRI would show that and the damage would have to be repaired under laproscopic surgery (i.e. tie the ligament back to where it belongs etc). However, a gross tear is pretty unlikely if you have no memory of a big. painful rip. More than likely, the MRI will show a little darkening of some constituents of the rotator cuff, inflammation of the RC. The treatment would be rest with no lifting and anti-inlammatories (naprosen, ibuprofen, etc) as mentioned above. So the MRI would probably not be well-covered right now, and you probably would get told to try rest and anti-inflammatories anyway. I'd probably do that first (I've had plenty of RC problems myself over the years, mostly from wrestling not bbing). If no relief, then maybe spring for an MRI, or get one as it would be a little more "medically necessary" at that point.
You did not mention if you are taking anything. Winny in particular can create crippling rotator cuff problems (and knee problems) in susceptible individuals, it has to do with depletion of the synovial fluid (fluid in the joint capsule).
Also, you need to consider seriously looking at your training. I saw your other thread where you are getting advice for a comp BB; this is good. Most shoulder problems I see in BBers is caused by improper benching, flaring the elbows out as you lower the weight eccentrically, which opens the rotator cuff at the same time as it is subjected to maximum weight and stretch -- a recipe for disaster. Pressing behind the neck is another cause, but a lot of people know this now, so you don't see this so much. I strongly suspect your training could be more rotator cuff friendly. Dips are a big problem in some individuals, but even with my shoulder problems I do weighted dips fine. I would say look at your benching first, this is often the culprit. Interestingly, fixing your form at first lowers your weight, then you sail up. A lot of shoulder-flarers have this wall at 275lbs they can't pass . . . Be careful with dumbbell presses too, and remember where the barbell would stop, stretch a little past that (that's why people do dbs after all . . .) but not too far. You might try joint supps etc, as some swear by them (even fellow orthopods).
I am not an orthopod, so I can't swear by this. But this is my 2c. Maybe an orthopod or chiro might chip in.