Excruciating pain in gums. Help?

ANUG or ANUP. You may develop acute necrotizing ulcerative gingivitis or periodontitis, a gum condition of which chronic severe bacterial infection kills the gum, cause them to ulcerate and die (burnt interproximal papilla on the tip, bad breath, and severe bleeding). See your dentist for cleaning, antibiotic, and follow ups.
Abscess. Could be infection from your tooth or the gums from periodontal disease that is putting pressure in the bone or space around the tooth. You need to see a dentist to be examined and treated.