All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible for you to try and treat your fiancée through Sharee‘ah-approved Ruqyah, as it was narrated on the authority of Jaabir that the Prophet, sallallaahu ‘alayhi wa sallam , said that Allaah did not create an ailment without a cure. He, sallallaahu ‘alayhi wa sallam, added that when a proper remedy is applied and there is no impediment, the ailment is cured by the permission of Allaah The Almighty. [Muslim]
It was also narrated on the authority of Abu Hurayrah that the Prophet, sallallaahu ‘alayhi wa sallam, mentioned that Allaah The Almighty created cures for all the ailments he created. [Al-Bukhari and Muslim]
It was also narrated on the authority of Ibn Mas‘ood that the Prophet, sallallaahu ‘alayhi wa sallam, stated that Allaah The Exalted did not create an ailment without creating a remedy for it and the remedy could be known to some and unknown to others. [Ahmad].
However, you must stay away from sorcerers and charlatans because they never do any good. It was narrated on the authority of one of the wives of the Prophet, sallallaahu ‘alayhi wa sallam, that he forbade Muslims from going to soothsayers and threatened that whoever did so, Allaah The Almighty would not accept Salah (prayer) from him for forty days. [Muslim]
With regards to the objection of this girl's family to sending her to persons for treatment, if you mean sorcerers and soothsayers then this is her family's right and duty and you should encourage them in this because, as we mentioned, sorcerers and soothsayers never do any good. Rather they will cause her to become sicker.
However, if you mean treating her using Sharee‘ah-approved Ruqyah, then they should not refuse. If the young woman is your wife you may decide, but if you are still her fiancé, as it appears, then you can only advise them.
Allaah Knows best.