Okay so here is what I think the bangle scene symbolizes. Sorry in advance if it sucks.
Khushi wears the bangles -which symbolize Shyam- even though she knows that it's not right for her cause her previous bangles are broken, that is, her babuji is sick. Arnav can't believe she's wearing the bangles/getting engaged.
Khushi: atleast he gave me bangles
Read- atleast Shyam offered to marry me. My father is sick, him and bua want to get me married. I didn't really have an option and it's not like you
Proposed, you moron.
And she gets engaged and is hurt when she finds out the truth. The bangle doesn't fit.
The broken piece of bangle is Shyam. He's stuck to Khushi and causing her great pain. When Arnav gets to know that she's hurt, he stops everything in his life (stops the car) and first screams at her/gives her pain cause he can't believe her naivety. How could she let this happen to her?! [:O]
Then he realises his error and tries to sooth her pain by tending to her injuries despite Khushi's attempts to ward him off. He tries to clean her wounds but still unintentionally hurts her initially. Then he picks Shyam out of khushi's life in the most barbaric way possible. Spits his remains outside his house (spits bangle onto the road).
And khushi is Shyam-free and pain-free again, unable to believe this man is the same ASR who had tried his best to make her life hell!!!
Such is love!
*dreamy sigh*
PS sorry didn't know what to do with NK