No, but if you visit your Threads page (link at the top of every page) you can see any replies to any of your comments. There's nothing special that marks a new reply, though.

I have a habit of upvoting nearly every reply anyone makes to any comment of mine, as a way of thanking them for the comment. This also happens to help when I skim my Threads page, since it's easy to spot comments that still have the voting button(s).