Are women obligated to count Sefira?
The shulchan aruch clearly says that women are exempt from mitzvos that are confined to time.
However the Rama in Shulchan Aruch says that women may fulfill those Mitzvot with the appropriate blessing.
The Sefadrdim follow the Shulchan Aruch and do not make a blessing on the above Mitzvot. The Ashkenazim follow the Rama and the women do make a blessing on those Mitzvot.
The Chofetz Chaim in his Mishna Berura suggests that women should not make a Brocho when they count the Omer though on other time confined Mitzvos they can.