Can an injury while tapering cause PMR symptoms?

I caught my finger in a closing door causing significant pain. I was 4th day of new dose-10.75 mgm pred from 11.5. Yesterday my shoulders started really hurting so I went back to 11.5 with relief. How long to stay there? I considered, after say 4 days, alternating 11.5/11 for how long? I am comfortable now. 

Pmr diagnosed Dec 2015; started at 15 snail pace reduction. No other symptoms. I also had a stress from a "black sheep adult child" no longer ongoing.

I would stay on that dosage at least a week. If you feel good then taper to the next dosage. I would do each taper every 2 weeks and then decrease again. I assume your doctor is sending you for blood work. I've been getting blood work every 6 weeks for the last 2 years. This is the first time I am going for blood work after 8 weeks and then back to the doctor.

And, I think your injury can affect your PMR.

I've found that any kind of stress can trigger a PMR flare, whether it is emotional or physical.

If you are comfortable on your current dose then I would stay there for a week.  You are close to the point where you are asking your adrenal glands to wake up and so some work and it is likely that they don't want to.  Suggest that then you alternate the dose as you said for 10 days and then get to your previous dose level.  If you feel ok, then continue to taper as before, but you are around the 10mg sticking point, so be wary.