Possible Clues:

• It's usually used in twos
• 'Hair of the dog' alternative
• Ache aid
• Trademark of 1899 that's no longer protected
• Drug discovered in 1853
• Endless longing for painkiller
• Mostly hoping to find an answer to pain?
• Hoping not to finish pain medication
• Bad sprain: one's ingested painkiller
• Common anti-inflammatory