Dental Abscess or Periapical Cyst: Given the location under the right mandible and the description of a painful soft lump, a dental abscess or periapical cyst is highly plausible. These conditions often result from dental infections and can cause localized pain and swelling.

Lymphadenitis: Inflammation of the lymph nodes, which could be due to a bacterial or viral infection, is a possible cause for the painful swelling under the mandible.
Sialadenitis: Inflammation of the salivary glands, which could be caused by a blockage or infection, might present with painful swelling in the area of the salivary glands, including under the mandible.
Sinusitis: Although the patient does not have cough or fever, acute sinusitis could still be considered, especially with the mention of swelling at the right sinus area. Sinusitis can cause referred pain and swelling to the face.

Ludwig's Angina: A severe infection of the tissues in the neck, which can cause significant swelling and pain. It's a medical emergency due to the risk of airway obstruction.
Deep Neck Infection: Infections in the deep spaces of the neck can be life-threatening due to their potential to compromise the airway and cause sepsis.
Malignancy: Although less likely in a young patient, malignancies such as lymphoma or metastatic disease to the lymph nodes or salivary glands could present with similar symptoms and should not be overlooked.

Branchial Cleft Cyst: A congenital anomaly that can present as a painful lump along the anterior border of the sternocleidomastoid muscle, which could be considered in the differential for a lump under the mandible.
Actinomycosis: A rare bacterial infection that can cause chronic abscesses or masses in the face and neck, which might be considered if other diagnoses are ruled out and the condition persists or recurs.