This is just a wild stab, which I can't verify unless you can share a model that exhibits the problem:
Could it be that the edges you have drawn are not actually coplanar, that is, that endpoints differ slightly in z? This is a common occurrence unless you are scrupulously careful while tracing lines on an image. Depending on the amount of z difference, the viewing direction, and the zoom level, small departures from a plane can be hard to see. If this is the cause, there are extensions that can flatten your edges to a single plane - search sketchUcation and the Extension Warehouse.
Upgrading to Pro will have no impact on this problem. It does not change anything about the way geometry is represented in the model or include any additional tools for healing problems.