Washing one's clothes during the week of Tish'ah BeAb (Shabuwa' SheHal Bo) is not permitted, even if they will not be worn till after Tish'ah BeAb. However, this prohibition does not only apply to the clothes that one wears but also to bed linen and towels and the like.
Some permit washing clothes for little children till the age of three because they are soiled regularly and one may not have enough replacements. Those who follow this leniency must be careful not to wash too many at once and may not do so in public.
Even though, nowadays, washing is generally done in a washing machine and not by hand it is still forbidden. Ironing previously washed clothes and bed linen is similarly prohibited at this time.
The custom of Ashkenazim is to forbid all the above from Rosh Hodesh.
(See Sh. 'A. 551:3, with Rema. Ben Ish Hai, 1st year, Parashath Debarim, Oth 6. Maamar Mordechai of H"R Mordechai Eliyahu, 25, Oth 65-67)
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