Injection in my finger to numb it but still felt pain. again, dentist removed some cavitys but after 3 injections i still felt pain. any worries ?

Great question!: First off: nothing to worry about. Personal observation and medical journals do reveal that a significant number of patients are less-susceptible to local anesthetics. Interestingly, not all anesthetics are the same: Mepivicaine seems to have better results in patients who don't respond well to bupiicaine or lidocaine; if you need a local again, you can request that by name.