Anyone who suspects demonic possession could seek the assistance of an exorcist. The first step would be to contact your diocese who may either have one or direct you to one at the appropriate time. Understand, however, that psychological illness will first have to be ruled out. While many cases of suspected demonic possession are reported, only rarely do any of these cases end up being attributed to demonic activity.
The following is from the Catechism of the Catholic Church:
". . . The solemn exorcism, called "a major exorcism," can be performed only by a priest and with the permission of the bishop. The priest must proceed with prudence, strictly observing the rules established by the Church. Exorcism is directed at the expulsion of demons or to the liberation from demonic possession through the spiritual authority which Jesus entrusted to his Church. Illness, especially psychological illness, is a very different matter; treating this is the concern of medical science. Therefore, before an exorcism is performed, it is important to ascertain that one is dealing with the presence of the Evil One, and not an illness (1673).