Praise be to Allah.
It should be noted that music is haraam and it is haraam to work in this field, be paid for it or teach it.
It was narrated from Abu Maalik al-Ash’ari (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said: “At the end of time there will be people among my ummah who regard adultery, silk, alcohol and musical instruments as permissible.” Narrated by al-Bukhaari.
This hadeeth clearly indicates that adultery, silk, alcohol and musical instruments are haraam, because the Prophet (peace and blessings of Allaah be upon him) said: “They will regard as permissible” and regarding as permissible can only come after something has been forbidden.
The fuqaha’ have stated in their chapters on buying and selling that it is haraam to sell musical instruments.
Music is haraam, and so is working in this field, learning it and teaching it. The money that is earned from that is haraam. May Allaah reward you for refusing to teach this haraam subject to the students and teaching them something that will benefit them, and leaving them to do things that will benefit them. Keep on trying to get your bosses to move you to an administrative post or to teaching something permissible. Do not give up, keep trying time after time, and ask Allaah to help you. Pray qiyaam and offer du’aa’ to Allaah, and ask Him to open the hearts of the bosses so that they will respond to your request.
With regard to the salary that you have earned:
The basic principle is that it is haraam because it is in return for haraam work, which is teaching music.
But seeing as you are not doing this haraam work, and you are trying to benefit the students, which is good for you and for them, we hope that there is no sin in your taking this salary, in sha Allaah. You can form a good intention if you stay in this place, because your being there is more beneficial for the students tham your not being there, because they may bring in teachers who do not fear Allaah and who would teach them music.
May Allaah help you to do that which He loves and which pleases Him.
And Allaah knows best.