hello thanks for the consult at hcm,,since it was after you bit the lip --it could be due to trauma--ulcer,,since carmex has not helped it to heal,,only lip chapping has reduced ,,but burning sensation has still not reduced,,i think you might have had
herpes labialis to begin with and then infection must have spread to the gums called herpetic ulcers,,either ways plz refer back to a oral physician for a check up and treatment,, you may need
antiviral topical therapy if it viral infection,,you can apply topical
anesthetic to reduce the burning sensations,,if it bacterial etiology you might need topical antibiotics like
metronidazole ,,for which prescription has to be under the guidance of oral physician,,hope it helps,,take care,,,