It is not that unusual for a dental injection to cause the sensation of a mild electric shock when administered, which could be the "popping" sound you refer to. This phenomenon occurs in roughly one out of 100 injections, when the needle passes directly through the nerve fiber, and is most common when anesthesia is required to numb the lower jaw. The nerves most commonly involved are the lingual nerve, which gives sensation to the tongue, and the sensory branch of the inferior alveolar nerve, which gives sensation to the lower teeth, jaw, gum and lip. In the vast majority of cases, the nerve is not damaged in any way from the injection, and in fact, the nerve is numbed so well that the dental procedure is usually completed painlessly.
If your tongue was numb, then you would have sustained injury to the lingual nerve, however you say that the numbness and tingling is under your chin leading up to your ear, which indicates the inferior alveolar nerve. A minor nerve injury results in the feeling of tingling or a "tickling" sensation. Remember a minor injury is just that.....it's minor, which is good. The fact that you're experiencing a lot of tingling is a sign that the nerve is healing itself. Usually the situation clears up by itself within six months. Unfortunately when a nerve is traumatised, it can take this long to regenerate itself. It may just need another 2-3 months before it feels totally normal again. Remember, the good news is that the tingling sensation is definitely a good sign.
All the best for your recovery.