[robocat]

Your seem to be using “chip on the shoulder” to mean “being overly proud”: is your usage common in your circles or is it a mistake? https://grammarist.com/idiom/chip-on-your-shoulder/

[demopathos]

My anecdotal usage is a combination of these two. Until I saw your provided definition I would have described chip on my shoulder to mean a sense of superiority that leads to me be rude or difficult to interact with.