Please be reassured that there are sensory nerves that are unavoidably cut, irritated, and stretched by the surgical process of creating a pocket for the implants, as well as the resultant tissue de-stretch, swelling decrease, and gradual return to normal as healing occurs. Burning, itching, tingling, and sharp "static electric"-like sensations are all described by patients. Every patient will have different sensations (or lack thereof), and will describe them differently!
Desensitizing massage is a good idea, but don't worry, this sensation is not permanent! It may actually get worse before it gets better (sorry), but it WILL gradually go away over several months and return to normal (a "new normal" you can happily live with). As healing progresses, these sensations will diminish and gradually subside.
You need not fear about this! Honest!