Traumatic Irritation or Aphthous Ulcers: This is the most likely diagnosis due to the common occurrence of minor injuries or irritations to the tongue, which can cause red papules. Aphthous ulcers, also known as canker sores, are another possibility and are very common.

Oral Candidiasis: This fungal infection can cause red patches and papules on the tongue and other parts of the mouth, especially in individuals with poor oral hygiene, denture wearers, or those with compromised immune systems.
Allergic Reaction or Contact Stomatitis: An allergic reaction to food, dental materials, or oral care products can cause red papules on the tongue.
Viral Exanthem: Certain viral infections can cause a rash or red papules in the mouth, including the back of the tongue.

Oral Cancer: Although less likely, it is crucial not to miss oral cancer, which can present with red, white, or ulcerated lesions on the tongue. Early detection is key to successful treatment.
Infectious Mononucleosis: Caused by the Epstein-Barr virus, this condition can lead to oral manifestations, including red papules on the tongue, along with systemic symptoms like fever and lymphadenopathy.
Secondary Syphilis: This sexually transmitted infection can cause a variety of oral lesions, including red papules, and it is essential to consider it in the differential diagnosis due to its potential for serious complications if left untreated.

Erythema Multiforme: A rare, immune-mediated condition characterized by target-like lesions on the skin and sometimes the mucous membranes, including the tongue.
Pemphigus Vulgaris: An autoimmune disease that can cause blistering of the skin and mucous membranes, leading to red, erosive lesions in the mouth, including the tongue.
Lichen Planus: A chronic inflammatory condition that can affect the mucous membranes inside the mouth, leading to red, white, or lacy lesions, although it more commonly affects the cheeks and gums.