Are women obligated in counting the Omer?
They are not obligated as it is a time based mitzva. However many women try to count anyways. If a woman is not sure that she will remember to count every night, (she doesn’t have someone to remind her to count etc.) it is better for her not to count with bracha. Sefardi women, that don’t make a bracha on a mitzva sh’zman grama, do not count with a bracha
O;CH 489 M:B 3, Orchos Rabeinu 2- pg. 92. O:CH 589-6.