Laundry during the Nine Days for Medicinal Purposes

Question

The Shulchan Aruch (OC 551:3) rules that one may not do laundry during the Nine Days, because it's taking one's mind away from the mourning.

1. Does this apply to doing laundry for medicinal purposes? Say that a person has dust allergies and needs to wash his pillowcase to get the dust off of it. Is that permissible? On the one hand, he's not doing it for pleasure; he's doing it out of necessity. On the other hand, so is washing your only set of clothes, which the Shulchan Aruch (same se'if) prohibits.
2. If yes, is one allowed to wash other linens while he's at it? On the one hand, he's removing his mind from the mourning by washing it. On the other hand, the real reason he's doing the laundry is for medicinal purposes.

Answer 1

Related: Permissible laundry during the 9 days

One answer there said (edited to shorten it):

My daughter had lice on the afternoon before Tisha b'Av. The protocol is to launder all the clothes that might have lice or lice eggs on them. I called Rabbi Barry Fruendel of Kesher Israel Congregation in Washington, D.C. He said that not only could I launder all of the clothes in our house on Tisha b'Av, I had to do the laundry because it was a health issue.

Your case is dissimilar insofar as you have prior knowledge of the problem and could wash or purchase sufficient pillowcases before the nine days.

The Ohr Someach website says that the only leniencies for medical reasons are:

Bathing in cold water for medical reasons or to remove dirt or perspiration is permitted. (Where cold water is required, hot water may be added to cold water as long as the mixture is not comfortably warm.) Soaping or shampooing and washing with hot or warm water are prohibited - unless it is required for medical reasons or to remove the dirt and perspiration. Swimming is prohibited except for medical reasons. Similarly, one may take a quick dip in a pool to remove dirt or sweat.

So there seems to be no clear exception to the custom of not laundering in the nine days. CYLOR.