If the dentist gave me a 2nd degree burn on my lip  and I now have a scar, can I sue him in small claims court?

Before filing a lawsuit, you want to complete your medical treatment for the second degree burn and when released by the doctor, obtain your medical bills, medical reports and documentation of any wage loss.  File your personal injury claim with the dentist's malpractice insurance carrier.  Your personal injury claim will include the medical bills, medical reports and documentation of any wage loss.  Compensation for the medical bills is straight reimbursement.  Compensation for wage loss is straight reimbursement.  The medical reports will document the nature and extent of your injury and will be used to determine compensation for pain and suffering, which is an amount in addition to the medical bills.

If the case is settled with the dentist's malpractice insurance carrier, NO lawsuit is filed.  If you are dissatisfied with settlement offers from the dentist's malpractice insurance carrier, reject the settlement offers and file your lawsuit for negligence against the dentist.  You don't want to file in Small Claims Court because of the limitations on the amount you can recover.  You should file in a higher court such as Superior.  Your state might have a different name for Superior Court.  If the case is NOT settled with the dentist's malpractice insurance carrier, you will need to file your lawsuit for negligence against the dentist prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.