There is a discussion amongst the Poskim regarding if one may recite the Bracha of “SheHechiyanu V’Kiyimanu LaZman Hazeh” during Sefira, or is it like during the three weeks (when we mourn the Churban) when this Bracha is not said.
The Mishna Berura (493:2) maintains that if one finds him/herself in a situation that calls for the recital of SheHechiyanu, they may indeed make the Bracha. (Some Poskim deduce from the Mishna Berura’s language that he held that one should try not to find him/herself in such a situation, if possible. Other Poskim argue and maintain that it can be recited L’Chatchilah, as the mourning of Sefira is not as stringent as the mourning over the Bais HaMikdash that we do in the 3 weeks before Tisha B’Av.)Although there is no real Halachic source in the Gemara, Shulchan Aruch or in the early Poskim to prohibit the recital of SheHechiaynu, some people do in fact have the custom not to recite it based on kabalistic reasons.
One who indeed has this minhag should continue keeping to it. As with everything, a Rav should be consulted for Halacha l’Ma’aseh. (See Sefer Likutei Maharich for further sources about this.)