How to prevent filling getting squeezed out of chocolate coated candies?
If I had to guess I would say your filling is not cold enough when you dip it so it starts to melt and pockets of air form when it comes into contact with the warm chocolate, which then doesn't cover the egg properly, causing filling to leak when it warms up a bit.
Try putting the fillings in the freezer for a bit (30 minutes to an hour) after you've shaped them, if possible. This will allow the chocolate to harden far quicker since the filling is much cooler, it should potentially stop the leakage (assuming the problem is the temperature).
For a nice looking coating of chocolate, try adding some cocoa butter to your melted chocolate. This will add a glistening sheen.