I'm not sure about the difference in use of the words みがって and わがまま. The both could be used as nouns and na-adjectives and both describe selfishness and egoism.  I already knew the word わがまま, so みがって is the new one here.  To make it easier to remember - a manga title to go with each word.

  • 身勝手 --みがって-- (adj-na,n) selfishness; egoism; egotism

身勝手なあなた by まさお三月 (Masao Sangatsu)

  • 我儘--わがまま-- (adj-na,n) (1) selfishness; egoism; self-indulgence; wilfulness; willfulness; (2) disobedience; (3) whim;

わがままロメオ by あじみね朔生 (Ajimine Sakufu)