Rinse the chicken wings well and add to a pot. Squeeze half a lemon on top and add of salt. Toss well, then cover with fresh water. Bring to a boil and let boil for 8 minutes.
Pour the water from the pot and rinse the wings. Cover again with fresh water and bring to a boil. Boil for 5 minutes, then pour the water and rinse the wings.
Return the wings to the pot and cover with fresh water. Squeeze a whole lemon or lime, add onion, salt, celery, garlic powder, pepper flakes, and all spice.
Return to the stove and allow to boil for 10 minutes. Drop the heat to medium and add the potatoes and carrots. Let simmer for 10 minutes until the veggies are soft.