Yes, is the short answer. However, that specialist could be anyone who has a vast experience of treating patients with PMR successfully. Usually this is a rheumatologist, but your GP or a geriatrician, neurologist, ophthalmologist may all be experts in this.
PMR is a condition where your shoulders become achy and there is not one single test that can prove the diagnosis. On the flip side, there are many conditions that can cause that manifestation – rheumatoid arthritis, cancer, giant cell arteritis, myositis, rotator cuff tendinopathy can all cause similar looking symptoms. Therefore, it is vital to do tests prior to starting steroids. Steroids will make the symptoms of all of these conditions better whilst making diagnosis more difficult (because the symptoms have been masked by the steroids). You may find it much more difficult to come off the steroids without the underlying condition being recognised and treated appropriately.
GCA is an emergency and should be treated immediately with steroids. However, even in this emergency it is of extreme importance to get blood tests prior to starting steroids. In an ideal world, you would be seen on the same day by the expert and all the tests would be done prior to starting treatment.