soothing the pain with a solution of cocaine-adrenaline
Not to be recommended, frankly, without getting a doctor to look at the eye(s) first.
Two other points : (1) the OP never even mentioned pain in his post (most conjunctivitis is described as "
uncomfortable" at worst), and (2) such a solution would only be available in the UK with a prescription anyway (cannot speak for other countries, obviously).