cherrybim,
The source I quoted has R’ Moshe being machmir on music during the year, but acknowledging that there are those who are meikil. He states clearly, though, that it’s assur during sefirah, so I’m not sure why it would be a tzorich iyun.
If you could please do me a favor, ask your rav if R’ Moshe’s heter because of nervousness is written in a teshuvah or something heard al peh. (I’m not asking you to question the veracity of what your rav said, c”v, but it’s easier to apply the heter to a specific situation if one could see the wording.)