Washing clothes is ossur during the 9 days in order that a person shouldn’t be masiach das from the aveilus of the 9 days. However if a person needs for himself (not for his children) clean undergarments or perhaps all of shirts are completely dirty and can’t be worn at all, is there any heter for him to wash these articles of clothing?
In the event that a person runs out of clothes, the preferable advice is to wash the clothes “locally,” taking out stains by washing with water, and with soap if required. This is not considered full “laundry,” and is therefore permitted.
It this is not possible, and one has absolutely nothing clean to wear, it is permitted to wash the minimum amount of clothes needed for the duration of the Nine Days. It is better to do this before before the Shabbos before Tisha Be’Av (before the onset of “shavu’a she-chal bo”; this year, there is no “shavu’a she-chal bo.”)
Preferably, clothes should be washed together with a load of children’s laundry.
For the concept of “local washing” to remove stains, see Gesher Ha-Chaim 21:10-11 concerning an aveil, and the same will apply here; see Hilchos Chag Be-Chag 4:14.
If one has no clothes to wear, it will be permitted to wash the minimum amount, because of kevod ha-brios.