A local anesthetic injection placed into an area of active inflammation did not work. What is the most likely reason?

Inflamed/infected tissue has a lower (more acidic) local pH. Local anesthetics need to be in their uncharged (lipid-soluble, base) form to cross the nerve membrane; in an acidic environment, a much higher proportion of the anesthetic remains in its charged (ionized) form, which cannot effectively penetrate the nerve sheath — reducing anesthetic efficacy even with technically correct technique and adequate volume.