Ingrown toenail with secondary infection: This is the most likely diagnosis given the symptoms of an ingrown toenail (hyperkeratotic tissue, pain, bleeding) combined with signs of infection (purulent fluid). The presence of purulent fluid indicates a bacterial infection, which is a common complication of ingrown toenails.

Onychocryptosis: This condition, also known as an ingrown toenail, occurs when the nail grows into the surrounding skin, causing pain, swelling, and sometimes infection. The hyperkeratotic tissue and pain are consistent with this diagnosis.
Paronychia: An infection of the skin around the nail, which can be acute or chronic. The presence of purulent fluid and bleeding suggests an acute paronychial infection, possibly secondary to the ingrown toenail.
Cellulitis: A bacterial skin infection that can occur in the foot, including around the toenails. While less specific than the other diagnoses, the presence of pain, redness (implied by the context), and purulent fluid could suggest cellulitis, especially if the infection has spread beyond the nail area.

Osteomyelitis: A bone infection that can occur if a skin infection (like an infected ingrown toenail) spreads to the bone. This is a serious condition that requires prompt treatment to prevent long-term damage. The presence of significant pain and signs of infection warrants consideration of this diagnosis.
Diabetic foot infection: Although the patient's age and the information provided do not specifically suggest diabetes, it's crucial to consider this in any foot infection, especially if there are signs of a severe infection. Diabetic foot infections can be more dangerous due to neuropathy and vascular disease.
Methicillin-resistant Staphylococcus aureus (MRSA) infection: MRSA can cause skin and soft tissue infections, including those around the toenail. Given the severity of the symptoms and the potential for antibiotic resistance, considering MRSA is important, especially if the infection does not respond to initial treatment.

Squamous cell carcinoma: Although extremely rare, long-standing ingrown toenails or chronic infections can very rarely be associated with the development of squamous cell carcinoma. This would be an unusual presentation but should be considered if the lesion does not heal with standard treatment.
Tuberculosis: Cutaneous tuberculosis can manifest in various forms, including around the nails. However, this would be an uncommon presentation and typically associated with systemic symptoms or known exposure to tuberculosis.