After Implant Surgery the Tooth Next to It Started to Move with No Indication of Periodontal Diseased and It HURTS?

There could be a few different issues going on. If you had a tooth removed and an implant placed, then the bite pressure may have changed when the one tooth was removed. That usually doesn't cause an infection however. After surgery many people clench their teeth more. That can cause a tooth to move, but again not usually an infection.

If the roots of the teeth in that area are close together then pressure from the implant could affect the nerve of the other tooth. It doesn't usually cause an infection, but it's not impossible.

I suggest visiting an Endodontist (root canal specialist). They can evaluate whether the nerve in the painful tooth is still healthy. It's possible if you are having that much pain, that the tooth needs a root canal.

Good Afternoon, I would suggest getting an x-ray or CBCT scan ASAP.  You need to see if the implant was placed too close /into the adjacent tooth.  I would recommend getting this done as soon as you can.  Good Luck.