It's a difficult sentence to translate, with some old-fashioned idea.
분에 넘치는 배부른 투정을 했는지도 모르겠다.
= I might have overstepped my bounds and thrown a bourgeois tantrum.
= I might have forgotten my proper place and complained for no reason.
* 분에 넘치다 = go out of one's rightful place/boundaries. (분 or 분수 is like one's "lot" in life).
* 배부른 투정 = (lit.) well-fed person's tantrum => well-heeled person complaining on petty things.
* -ㅆ는지도 모르겠다 = I might have (done something).