Hi, I'm no doctor but I think you developed knots in your shoulder trigger points, probably in the neck as well, since they're working very closely.
This may happen for many reasons: small injury that went unnoticed, muscle imbalance, lifting too heavy when you're not yet ready. It results in some muscle (normally inner supporting muscle) going weaker and the other muscle overcompensating, so normally MRI won't show much. In some serious cases it can be due to joint problem, but from what you're describing doesn't sound so.
If this has been now going on for a while you should benefit from two things:
1. A few upper back, shoulder and neck massage or accupuncture or both.
2. Stop your usual upper lifting routine immediately. Ideally have a physio consultation so they can have a look on which muscle is week and advice you on what exercises to do to "switch" the "lazy" muscles back on. There are some really amazing exercises with resistance bands and self massage with a tennis ball. Have a look on YouTube.
I had the same thing so talking just from experience and what I read ;)
Also, don't wanna blame and shame but I can't get my head around why your trainer didn't advice you to do so. That should have been the first thing they told you after you mentioned stiffness and pain.;)
Maybe your doctor is right. I have a chronic neck problem which has gotten really bad over the last couple of years, and weight lifting doesn't help it, though it does help me because I have so many injuries there's not much left to do. But when my shoulder hurts, it's not the shoulder, it's pinched nerves from the neck. Now, in my case, I've known for years I have deterioration in the discs in my neck, probably from an old auto accident. I was sent to physical therapy for the neck and the arms and shoulders, and it worked for a while, but only when I stopped weight lifting (in my case, my arms hurt so bad I really had no choice). As soon as I started lifting again, and I only lift light weights, it came back with a vengeance. At any rate, only an MRI would probably tell you where the problem is, and you'd probably be sent to physical therapy, and they would probably tell you to stop lifting weights and just do the stretches and exercises they give you until you're healthy again. My main point here is, it might not be your shoulder, it might be coming from the neck, and as long as you don't see a specialist you won't know, But if not lifting makes it go away, it's pretty clear it's either an injury or your trainer isn't training you correctly or you simply don't have the body necessary to lift or you're lifting a lot which makes you a serious athlete, and they hurt all the time especially as they age. What someone who specializes in sports medicine can tell you is how much mobility you have in your shoulders and your neck -- if you don't have much, you will hurt. Hope this at least gives you some ideas of what to investigate.