Lipoma: A benign tumor composed of fat tissue, which can cause tenderness, especially if it becomes inflamed or irritated. The description of the sore underarm looking like fatty tissue that is tender without redness aligns with the presentation of a lipoma.

Infected or inflamed sebaceous cyst: While the absence of redness makes this less likely, sebaceous cysts can become infected or inflamed, causing tenderness. They are common in areas with high sebaceous gland concentrations, like the underarms.
Folliculitis: An inflammation of the hair follicles, which can present with tender lesions, although typically there would be some redness. The underarm area is prone to folliculitis due to friction and shaving.
Hidradenitis suppurativa (early stages): This chronic skin condition can start with tender, painful lesions in the underarm area without significant redness in its early stages.

Breast cancer (including male breast cancer): Although extremely rare in an 18-year-old, any unusual lump or mass, especially if it's tender and in the underarm area (which could be related to the breast tissue), warrants consideration of breast cancer due to its potential severity.
Lymphoma: Enlarged lymph nodes in the underarm can be tender and might be mistaken for fatty tissue. Lymphoma is a serious condition that requires early diagnosis and treatment.

Madelung's disease (Multiple Symmetric Lipomatosis): A rare condition characterized by the growth of non-cancerous fat masses around the body, which could potentially cause tender lesions under the arms.
Dercum's disease: A rare condition characterized by painful fatty growths, which could potentially present in the underarm area, although it's more commonly seen in post-menopausal women.