Found it!!!

For many years, I have had images from this film burned in my brain.

I thought of the "punk girl with blond hair and dark makeup" tonight and decided to type punk into the search engine and found out finally the name of this movie!

Thank you to Breaking Glass for introducing a then 10 year old girl from Utah to punk music, thank you HBO for playing it, thank you mom for letting me watch whatever I wanted, thank you IMDB for your wonderful and useful website and thank you Hazel O' Conner for an UNFORGETTABLE performance!