You have a couple of choices here, depending upon what is exactly happening (which I don't clearly understand from your description).
If you are using the advanced labeling toolbar, you can data-define your label's location (using x, y fields in attribute table) and use the Move Label tool to manually position the label.
See linfiniti.com blog for info on using the new labeling toolbar.
If the label is not visible, because the new feature point has a higher priority, check the Show All Labels (i.e. including colliding labels) choice in the Engine Settings dialog of advanced labeling.
This will show the label, even if it overlaps something else, like another label or a feature.
Alternatively, if your points are overlapping, you may want to check out the Shift Points plugin, if you want to create a new shapefile with the points offset.
"Moves overlapped points in a circle around original position."