Pinworm Infection (Enterobius vermicularis): This is a common condition in children, characterized by intense anal itching (pruritus ani), especially at night, and can lead to burning sensations. The increased stool frequency could be related to the body's reaction to the infection.

Gastroenteritis: Viral or bacterial infections can cause increased stool frequency and may lead to anal irritation, resulting in burning and itching sensations.
Dietary Irritants: Consumption of spicy, acidic, or high-fiber foods can irritate the anal area and cause burning and itching, along with changes in stool frequency.
Atopic Dermatitis (Eczema): Although more commonly associated with skin lesions, atopic dermatitis can cause anal itching and irritation, potentially leading to burning sensations.

Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease and ulcerative colitis can present with increased stool frequency, anal irritation, and systemic symptoms. Missing this diagnosis could lead to significant morbidity.
Sexual Abuse: In cases of anal itching and burning in children, it is crucial to consider the possibility of sexual abuse, which requires immediate attention and intervention.
Food Allergies: Certain food allergies, especially to dairy or gluten, can cause gastrointestinal symptoms, including increased stool frequency, and may lead to anal irritation.

Threadworms (Strongyloides stercoralis): A parasitic infection that can cause gastrointestinal symptoms, including increased stool frequency, and anal itching.
Lactose Intolerance: While not typically causing burning, lactose intolerance can lead to increased stool frequency and potentially irritate the anal area, causing discomfort.
Anal Fissure: A tear in the lining of the anus can cause severe pain, burning, and itching, especially during and after bowel movements.