悩み is a simple noun, but 悩みごと is like a verbal noun. (contraction of 悩んでいること) And it gives a nuance that it is ongoing or temporary issue. More used in daily conversation. 悩みごとでもあるの？ - Are you having any troubles or something?? (to your friend who's been depressed for a while) 悩みごとは全部片付いたのでもう大丈夫です。- Now I'm ok, cause all my concerns have been solved!