Can one listen to music privately in your own car or with earphones during the omer?
Although there is no formal prohibition on listeing to music in a private manner (without communal singing and dancing), the common custom is to prohibit listening to music, and this should be upheld. However, the custom does not have the same stringency as communal singing and dancing, and it is permitted when a person requires music for therapy, for concentration (possibly, in a car), and so on.
Sources: See Iggros Moshe, Yoreh De’ah 2;137; Yecheveh Da’as 6:34; Tzitz Eliezer. All three write that one may not listen to music during the sefirah period.