Hello Stu,
"Ésta se hizo la importante conmigo" means that she acted like she is a very importan or busy person and have no interest in you.
Ésta: It is a despective word to say she, It's because "Esta" is the same as "it", He is treating her like and object.
Se hizo: It is correct what you said, made herself / acted like.
'La' importante: Well... it is hard to explain. It means that among a lot of people She is THE ONE person that is important. She is not an important person, she is THE IMPORTANT PERSON.
I hope it helps you!
Greetings!
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