There are various types of Sadaqah:
1) Sadaqah Waajibah (Obligatory Sadaqah) This is a charity given due to a vow (if Allah does so and so for me then I will give a certain amount of money in charity), or Sadaqatul-Fitr 9Sadaqah given at the end of Ramadhan), or interest money etc. The ruling for this type of charity is, that it can only be given to the poor and needy, and cannot be used for a Masjid or any other organisation.
2) Sadaqah Naafilah, or Lillah (Optional charity) Any other charity besides the above-mentioned is known as Sadaqah Naafilah or Lillah. This type of charity may be used for the purpose of building a Masjid or any other Ilsmaic organisation.
Women can give Sadaqah or Lillah. The person who mentioned this to you may have misunderstood the Hadith in which Rasoolullah Sallallahu alaihi wasallam ordered women to give Sadaqah due to the fact that he saw that the majority of Jahannams dwellers were women. (Mishkaat) In this Hadith Rasoolullah used the words, 'Give Sadaqah', but this does not imply that women should give Sadaqah and not Lillah. As stated above, Sadaqah Naafilah and Lillah are the same thing, therefore, the meaning of the Hadith is, 'give charity'! ie Lillah.
Damm will only be given if you are certain of a mistake you made during Umrah. If you only have a doubt, then an amount can be given in Sadaqah.
And Allah knows best.