New Daily Persistent Headache (NDPH): Given the patient's history of new daily persistent headache onset after a COVID-19 infection and lack of response to various treatments, NDPH remains a strong consideration. The condition is characterized by a persistent headache that lasts for more than 3 months, and its onset can be traced back to a specific event, in this case, the COVID-19 infection.

Chronic Tension-Type Headache: Although the patient has tried various treatments, the possibility of chronic tension-type headache cannot be ruled out, especially given the lack of response to treatments typically effective for other headache types.
Medication Overuse Headache: Despite the extensive list of treatments tried, the potential for medication overuse headache should be considered, as the frequent use of analgesics and other headache medications can lead to this condition.
Cervicogenic Headache: The patient's lack of response to cervical paraspinal and trapezius trigger point injections and cervical facet block does not entirely rule out cervicogenic headache, as these treatments may not always be effective or the diagnosis might have been missed.

Giant Cell Arteritis: Although less likely given the age and duration of symptoms, giant cell arteritis is a critical diagnosis not to miss due to its potential for serious complications, including vision loss. The patient's lack of response to prednisone might suggest this is less likely, but it should still be considered.
Brain Tumor or Other Space-Occupying Lesions: The persistence of headache despite extensive treatment warrants consideration of a brain tumor or other space-occupying lesions, even though the likelihood is low.
Intracranial Hypotension: This condition can cause persistent headache and should be considered, especially if there have been any recent lumbar punctures or epidural injections.

Hemicrania Continua: A rare headache disorder characterized by a continuous, unilateral headache with periods of exacerbation. The lack of response to indomethacin (not mentioned in the treatments tried) does not rule out this diagnosis entirely.
Trigeminal Neuralgia: Although typically characterized by episodic, severe pain, atypical forms can present with more constant pain, making this a rare but possible consideration.
Headache Due to Infectious or Inflammatory Conditions: Other rare infectious or inflammatory conditions affecting the central nervous system could potentially cause persistent headache and should be considered, especially given the onset after COVID-19 infection.