Hello, my name is***** and I have over 20 years of experience as a veterinarian.
I am sorry to hear that Eddie is repeatedly biting his bottom area.
He may be trying to lick or itch his perianal area after eating in response to a food allergy which can cause perianal itchiness.
Other reasons for perianal itchiness include constipation or diarrhea, fleas, tapeworms or other gastrointestinal parasites, full or infected anal glands or impaction of the glands.
I also want to mention a condition called perianal fistulas, although we see this more commonly in shepherds and other breeds with heavy coats and thick tails. This is a painful condition where dogs develop fistulous tracts around the anus and lick in response to the discomfort. It is likely an autoimmune mediated disease process (body attacks itself) as it responds to immunosuppressive drugs and while it cannot be cured we can usually control it. It is diagnosed via a biopsy coupled with a history of perianal inflammation and tracts.
Make sure that his stools are normal size and consistency and look for any signs of worm packets that look like grains of rice too. If he's had fleas at all in the past year then tapeworms are a real concern and then you may choose to treat for those with a wormer containing praziquantel. I would also recommend submitting a stool sample to check for other gastrointestinal parasites.
If he has had fleas even if you don't see them now I do recommend using protection. They are the most common allergen, often lead to rear body itchiness, and it only takes one bite a month to make an allergic dog lick and scratch excessively. I recommend using flea prevention even if you never see one again. Frontline Plus, Advantage II or Advantix are excellent. Don't use over the counter products, especially Hartz or Sargents, as most are ineffective if not toxic.
He should have his anal glands checked either by your veterinarian or an experienced veterinary technician to make sure they aren't a problem.
If he will let you she may benefit from a cool compress to the area, patting dry and then applying a light coat of cortisone cream (like Cortaid) to the area a couple times a day.
If he's been fed a new food or treats, or had table food my thought would be this is a food allergy. Treatment is topical cortisone and not exposing him to the allergen again. It can take a few weeks to get the allergen out of his system. If this has been going on a while perhaps he is allergic to his food and I recommend a hypoallergenic diet trial. You could try a true hypoallergenic diet like Hills z/d or Purina Veterinary Diets HA. No treats, flavored medication or bones while on the diet and it must be used for a least 12 to 16 weeks to see the full effects, though most owners see some improvement in 6 to 8 weeks.
Finally if he is having trouble passing stools then adding 1 to 2 tablespoons of pumpkin (not pie filling, just canned pumpkin) to each meal will help soften his stools and make them easier to pass and thus make him more comfortable.
Best of luck with your fellow, please let me know if you have any further questions.