The title says the question; counting the omer is a yearly mitzvah. Why do we not make a shehechiyanu bracha on the first night we count the omer just like we do on sitting in a sukkah for the first time on Sukkos, for example? Here are two answers…
1) The Rashba says that counting the omer is drawn from the main mitzvah of bringing the korban omer and the shtei halechem – both of which we do not bring without a beis hamikdash. The counting of the omer should thus cause us a degree of pain for it reminds us of the destruction of the Mikdash and so we do not say a shehechiyanu. This is also why immediately after countingwe say a ‘harachaman’ to rebuild the Mikdash.
2) The Ridbaz answers that sfiras ha’omer is a time of judgement [din], and was the time of the plague of the students of Rabbi Akiva. This is why we count at night which is a time of judgement, to weaken the attribute of ‘din’ which accompanies night. And we do not say shehechiyanu because this is not purely a time of simcha. And the end harachaman is so we should have the Beis Hamikdash and once again have true simcha in serving HaShem.