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No, the phrase "physician, heal thyself" is not attributed to Plato. It actually comes from the Bible in Luke 4:23.
Medic - 1954 Physician Heal Thyself 1-23 was released on:
USA: 11 April 1955
Mister Roberts - 1965 Physician Heal Thyself 1-3 was released on:
USA: 1 October 1965
One Life to Live - 1968 Physician Heal Thyself 1-10507 was released on:
USA: 21 August 2009
Chicago Hope - 1994 Physician Heal Thyself 4-24 was released on:
USA: 13 May 1998
Germany: 24 March 1999