No, I haven't experienced that.....
You give a very good description in your OP and it does sound like "Rotator Cuff Syndrome."....no big deal but painful and be difficult to treat.
Google it.
It is known by other names e.g Shoulder impingement Syndrome but basically it is damage to the muscles around the shoulder joint.
You haven't mentioned if you are taking any pain relief e.g Ibuprofen.
There are many causes, but sitting at a PC all day would be one to consider.
Continue the exercises, take Ibuprofen 600mgms as and when necessary up to 2,400 mgms a day and if there is no improvement after another 2 weeks, then see you GP as you will need X-Rays and possibly an Orthopaedic opinion.