My last post does not show up in my recent inbox messages.
But it does show up in a search.
Does it only show up if it has had replies?
If by "last post" you mean this, then you won't see anything in your inbox about this post unless you get replies to it or some other type of interaction (comments, answers, proposed edits, etc.).
New posts made by yourself won't show up in your inbox until some trigger happens to make a message in your inbox, and such triggers are typically the things I just stated (new comments on it, new answers, new proposed edits to the question, etc.).