Whether it falls under dental malpractice, which is a special category under personal injury, or some other category, if you have been injured due to sub standard medical care, then you may have a claim. These are not easy claims, but based on the facts that you have posted, I believe you owe it to yourself to obtain a consultation with a personal injury attorney who has handled dental malpractice claims in your jurisdiction.
Personal injury attorneys nearly always give a free initial consultation.
The insurance industry’s own statistics indicate that once an attorney becomes involved, the value of any claim at least doubles.
Put those two facts together and it is in your best interest to retain experienced legal counsel at your earliest possible convenience.
This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.
The permanently damaged nerve sounds like malpractice. The advertising issue may or may not be relevant, and it's certainly not as important as getting your dental work finished correctly.
See another dentist, and make sure you document the restorative work with photos and careful documentation so if legal action is necessary, you'll have support. if this 2nd opinion is that there was malpractice, see a medical malpractive lawyer.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.