The pastor of my church has been allowing a retired nun to give the homilies during Mass. Is this allowed?

No. Here is the relevant text from the General Instruction of the Roman Missal (revised edition, 2002):

The homily should ordinarily be given by the priest celebrant himself. He may entrust it to a concelebrating priest or occasionally, according to circumstances, to the deacon, but never to a lay person. In particular cases and for a just cause, the homily may even be given by a bishop or a priest who is present at the celebration but cannot concelebrate. (66)

As you can see, it is preferred that the celebrating priest gives the homily himself. In particular circumstances a bishop, deacon, or another priest can give the homily. But it is never to be given by a lay person.