Q. Is it true that according to the Shulchan Aruch women are not supposed to work during the nights after Pesach until Shavuos?

A. Shulchan Aruch (O.H. 493: 4) writes that women accustom not to perform any work from Pesach until Shavuos, from sunset onward. Mishna Berura (ibid. 18-19) rules that the above applies equally to men and quotes two reasons for this custom. Firstly, the Talmidim of Rabi Akiva were buried at that time, and when a Sage dies and is buried, all should abstain from work. Women are mentioned, according to this reason, because they took care of the burials.
The second reason is that the Torah labels the time of Sefira counting as days of rest (Sheva Shabbosois). Mor Uketzia (493) quoting Ramban (Vayikra 23: 36) adds that this period is seen as tantamount to the days of Chol Hamoed between two festivals, and some work restrictions apply.
Another reason quoted by Mor Uketzia (ibid.) is that one should not engage in work until he counts the Omer, to avoid forgetting to comply with the mitzva. (See other reasons mentioned in Bein Pesach Leatzeres).
Poskim (Chok Yaakov 493: 12, Kaf Hachaim ibid. Aruch Hashulchan, et. al.) mention that this tradition is mostly not kept in our days. They also maintain that even according to the ones that observe this tradition, it applies only to taxing and lengthy work, not to common housework. (Piskei Teshuvos 493: 16).
Horav Shlomo Miller’s Shlit’a opinion is that even those who do observe this tradition need not abstain from performing work after counting sefira.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a.