Can a new crown create a change in my occlusion? What are your suggestions to solve this? (Photo)

In all likelihood the crown was "too high" thus the grinding. It's very possible this produced movement of the disc of the TMJ complex, therefore you can't "open straight" anymore. In my opinion the crown needs to be removed and a new one placed that is in the proper occlusion. If the prepared tooth is very short a gold crown works very well in this situation. However my material of choice today is a full zirconium crown.

There may be an underlying issue as to why you had radiating pain down the side of your neck and upper back and arm weeks after your crown was placed.  If you are having any radiating numbness, I would see your physician immediately.However, I would also address your crown.  Your crown on #2 needs to be removed, and a temporary placed with the proper occlusion.  Your crown may have been very high, which could change the position of your TMJ disc.  I would not allow a permanent restoration to be placed until you no longer have radiating pain, and you are able to open your mouth without deviation to the side.  Having to do adjustments after permanent restorations are seated is normal, so this should be something you are very comfortable talking to your dentist about.

Your crown should probably be replaced.  Go back to your dentist yet again and don't leave until your bite feels normal again.  The extensive adjustments could damage the crown to the point of needing a redo, especially since the metal is already showing through.  These kinds of adjustments are common and your dentist depends on your feedback, so you should not feel uncomfortable addressing this with your dentist.