In this subsection of a multi-topic teshuva, Rav Moshe Feinstein deals with two issues. First, he addresses the question of whether it is permissible to listen to musical instruments during sefirah if you are alone. Rav Moshe says that it is forbidden, based on the fact that even during the rest of the year we are lenient about listening to instruments for the purpose of enhancing a simcha, and therefore the added prohibition of sefirah encompasses people who are by themselves. [It should be noted that Rav Moshe has a generally strict view about listening to music post-churban Beit HaMikdash, and thus his view in this case is strict as well]
Rav Moshe then deals with the issue of whether or not a woman can get a haircut during sefirah. The existence of such a question is based on the fact that a woman who is in aveilut can get a haircut after shiva but still during shloshim. Even according to the Ramo, who is strict when it comes to shloshim and the week of Tisha B'Av, Rav Moshe feels there is still room to be lenient since the prohibition of haircuts during sefirah is only a minhag (albeit a strong one). However, he writes that if there is no pressing need for the haircut then it should be avoided.