No.
The "free" insertion applies to the first 30 days only.
Now, it is quite possible that you will be eligible to "free" insertions when the automatic relist takes place after 30 days.
It is impossible to give factual answer, not knowing if you have a store or not and the category you list in.
Frankly, it would be easier in your case, when posting on this board, to use your real selling ID. There is no advantage in hiding it.
