You have damage to the Inferior Alveolar Nerve. If you are completely numb (like when you are given a novacaine shot), the nerve could have been severed. If not, and you have tingling sensations, that is a sign that the nerve could be repairing itself. You need to see an Oral Surgeon, not a dentist, for a 2nd opinion. Personally, after what I have been thru with a botched root canal, I would NEVER let a dentist pull a tooth or do a root canal. Unfortunately, it takes being injured before you learn that lesson.
Make an appt with an Oral surgeon NOW to find out what kind of damage was done to the nerve. If it is severed, you need to get it surgically reattached sooner rather than later. Be aware that sometimes when nerves are attached or even repaired, you can go from numbness to burning pain. Its a difficult situation to be in ... hard to know what to do .. but time is off the essence if you have a problem that won't repair itself.
There is some amount of nerve issues that are likely to occur from tooth extractions and many resolve by themselves. But, be proactive so you don't end up waiting too late for surgical intervention if the OS thinks that it is necessary. Besides, your issue is now above what a general dentist can adequately treat.