Praise be to Allah.
It is haraam to wear this necklace, because it is in the form of a Pharaonic key, and it is well known that the Pharaohs were kuffaar, and it is not permissible for the Muslim to wear anything on which there is one of the symbols of the kuffaar or anything that is unique to them. If we add to that the fact that it is in the form of the cross which is worshipped by the Christians, then this is another reason for it definitely being haraam.
It is haraam to use things on which there are crosses. The Prophet (peace and blessings of Allaah be upon him) used to alter things on which there were crosses. It was narrated that ‘Aa’ishah (may Allaah be pleased with her) said: “The Prophet (peace and blessings of Allaah be upon him) would not leave anything in his house on which there was a cross but he would alter it.” Narrated by al-Bukhaari, 5952.
This is in addition to the fact that wearing this necklace is imitating the kuffaar, which is forbidden in many ahaadeeth and reports, of which the following are the most important:
1 – The Prophet (peace and blessings of Allaah be upon him) said: “Whoever imitates a people is one of them.” Narrated by Abu Dawood, 3512; classed as saheeh by al-Albaani.
Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said: This at the very least indicates that it is haraam to imitate them, although the apparent meaning is that the one who imitates them is a kaafir. Iqtida’ al-Siraat al-Mustaqeem, 1/237.
2 – It was narrated that ‘Abd-Allaah ibn ‘Amr ibn al-‘Aas said: The Messenger of Allaah (peace and blessings of Allaah be upon him) saw ‘Ali wearing two garments dyed with safflower and he said: “These are garments of the kuffaar, do not wear them.” Narrated by Muslim, 2077.
Shaykh Ahmad Shaakir said in his commentary on Musnad Ahmad (10.19): “This hadeeth clearly indicates that it is haraam to imitate the kuffaar in one's dress, one's way of life and one’s appearance. There has been no scholarly difference of opinion on this point from the earliest generations.”
Ibn Taymiyah (may Allaah have mercy on him) said: “Imitating them in outward matters leads to imitating them in attitude and actions, hence we are forbidden to imitate the kuffaar, the Persians and the Bedouin, and both men and women are forbidden to imitate the opposite sex, as it says in the marfoo’ hadeeth: ‘Whoever imitates a people is one of them.’” Majmoo’ al-Fataawa, 22/154.
From the above we may conclude that it is not permissible to wear this necklace.
The Standing Committee was asked to issue a fatwa concerning the type of imitation of the kuffaar that is forbidden. They replied:
What is meant by the type of imitation of the kuffaar that is forbidden is imitating them with regard to those things that are unique to them, such as customs and beliefs and acts of worship that they have innovated in religion, such as imitating them by shaving off the beard… and the festivals that they have adopted; and exaggerating about the righteous by seeking their help, circumambulating their graves, offering sacrifices to them; ringing bells; wearing crosses around one’s neck or hanging them up in houses or having a cross tattooed on one's hand…
Fataawa al-Lajnah al-Daa’imah, 3/429.
They were also asked about a Muslim who wears a cross. They replied:
If he is told of the ruling on wearing a cross and that it is a Christian symbol, and he is told of the evidence that the one who wears it is happy to be regarded as one of them and approves of their ways, and he still persists in that, then he is to be regarded as being a kaafir, because Allaah says (interpretation of the meaning):
“And if any amongst you takes them (as Awliyaa’), then surely, he is one of them. Verily, Allaah guides not those people who are the Zaalimoon (polytheists and wrongdoers and unjust)”
It also implies that one agrees with the Christians and their claim that ‘Eesa (peace and blessings of Allaah be upon him) was killed, but Allaah denies that as He says in His Book (interpretation of the meaning):
“but they killed him not, nor crucified him, but it appeared so to them”
Fataawa al-Lajnah al-Daa’imah, 2/119
The questioner indicates in his question that there is a relationship between him and that girl, and it seems that this relationship is not one of marriage. This is a haraam relationship that is not approved of in Islam, because it is not permissible for a man to have a relationship with a non-mahram woman, and it is not permissible for a woman to have a relationship with a non-mahram man, because that involves doing things that Allaah has forbidden, such as speaking softly, looking, touching, being alone with a person of the opposite sex or immoral actions, and because it corrupts the heart and spoils one's relationship with Allaah and submission to Him, even if they do not have a haraam physical relationship.