Wearing the amulet (Ta’aweez in Urdu) is permissible in light of the Shariah.
The amulets which are prohibited in the Hadith are those which have (words of) “Shirk” (ascribing partners to Allah Ta’ala) in them.
There is a Hadith in Jame’ Tirmidhi, Sunan Ibn Majah and Musnad Imam Ahmed:
Translation of Hadith: Hadhrat Abu Khuzama (May Allah Ta’ala be well pleased with him) narrates on the authority of his father, he said that I asked the Holy Prophet (Sallallahu alaihi wa sallam): O Prophet of Allah! (Sallallahu alaihi wa sallam), please tell that the prayers which we recite, the medicines which we take and those things of protection, through which we protect ourselves, can all these change the fate decreed by Allah Ta’ala?
The Holy Prophet (Sallallahu alaihi wa sallam) said: These are all included in the fate decreed by Allah Ta’ala.
(Jame’ Tirmidhi, Hadith No: 2206; Sunan Ibn Majah, Hadith No: 3563; Mustadrak Alas Sahihain, Hadith No: 87; Musnad Imam Ahmed, Hadith No: 15870; Zujajatul Masabeeh, Vol.1 Babil Imani Bil Qadr.)
Also there is a Hadith in Sahih Bukhari:
Translation of Hadith: It has been narrated on the authority of Hadhrat Abdullah Bin Abbas (May Allah Ta’ala be well pleased with them), he says that the Holy Prophet (Sallallahu alaihi wa sallam) would give Imams Hasan and Hussain (May Allah Ta’ala be well pleased with them) in the protection of Allah Ta’ala with words:
Translation: A’audhu Bi Kalimatillahit Tammati Min Kulli Shaitanin Wa Hammatin wa Min Kulli Ainin Lammatin.
Translation: Hasan and Hussain, I give you in the protection of the words of Allah Ta’ala (i.e. the Asma Husna (99 names) of Allah Ta’ala, the divine books revealed by Allah Ta’ala and which are pure of every defect) against every rebellious, harmful genie and human being and against the harm of every harmful animal and against the harm of evil eye (Nazr bad in Urdu, which harms in many ways)
The Holy Prophet (Sallallahu alaihi wa sallam) would say:
Your father i.e. Hadhrat Ibrahim (peace be upon him) would recite the same Dua for Hadhrat Ismail and Hadhrat Ishaq (peace be upon them)
(Sahih Bukhari, Hadith No: 3371; Zujajatul Masabee,Babi Iyadatil Mareez )