Acute Tendinitis or Tenosynovitis: This condition is likely given the sudden onset of pain, swelling, and redness in the hand and wrist, especially if the patient recently engaged in repetitive activities or experienced a minor injury. The shooting/burning pain description aligns with inflammation of the tendons or their surrounding sheaths.

Sprain or Strain: A common injury that could result from overuse or a sudden twist, leading to pain, swelling, and limited mobility in the hand and wrist.
Cellulitis: Given the redness and swelling, cellulitis (a bacterial skin infection) is a possibility, especially if there's a history of trauma to the skin or an open wound.
Ganglion Cyst: Although less likely to cause acute pain, a ganglion cyst could become inflamed or ruptured, leading to sudden onset of pain and swelling.

Compartment Syndrome: A medical emergency characterized by increased pressure within a muscle compartment, which could lead to nerve and muscle damage. The severe pain, especially on movement, and swelling are red flags.
Infectious Arthritis: Bacterial or fungal infection within the joint, which is a serious condition requiring prompt antibiotic treatment to prevent long-term damage.
Osteomyelitis: Bone infection, which could present with pain, swelling, and redness, particularly if there's a history of trauma or immune compromise.

Gout or Pseudogout: Although more commonly affecting the lower extremities, these conditions can cause sudden, severe joint pain and swelling in the hand or wrist, especially in patients with a history of these diseases.
Scleroderma or Other Connective Tissue Diseases: Conditions like scleroderma can cause hand and wrist pain, swelling, and limited mobility, but these would typically be part of a broader systemic illness.
Neoplastic Processes: Tumors, either benign or malignant, could cause pain and swelling but would be less likely to present acutely without a history of gradual onset or other systemic symptoms.