Invisalign is causing me pain in my shoulder and neck.

While this can be a completely unrelated issue, it is possible that you are clenching on your aligners.
Accessory muscles in the neck can get tired and sore like any other muscle that is over used. It has zero to do with your teeth and everything to do with over using your muscles of mastication. I normally build bite ramps into my Invisalign aligners which avoids this all together.

This is not a normal occurance with Invisalign, but changing the position of the lower jaw and/or the way the teeth fit together can lead to the symptoms you are having.  I wonder if you have ever had neck and shoulder pain before, and if so when does it seem to happen?  Some people have bite disorders without symptoms but when something is changed in the bite, the symptoms can appear.  Do you clench and/or grind your teeth?  Do you suffer with headaches?  Do you ever have ringing in your ears or dizziness?  These are all symptoms that could be signs that you have an imbalance in your system.  

It is difficult to tell without seeing you to make a proper assessment.  I would suggest that you find a dentist who is knowledgeable about treating TMJ (temporo-mandibular joint) problems and see if they can find a link between your aligners and the symptoms you are experiencing.  (hope that is of some help)

The cause of the pain you are describing would be highly unlikely due to the wearing of Invsalign aligners.  The nice thing about invisalign is it is removable, so you could do a trial tho see if more incidences of pain and relief coincide with the times you wear the aligners and when you don't. I would recommend not wearing them for two weeks then start wearing them again and see if this unusual pain returns.

Douglas E. Jopling, DDS