The hard truth is that your options are limited, and it is worth knowing that going in so you are not spinning your wheels chasing solutions that do not exist.
What you are describing sounds like group punishment. When something happens in a unit, whether it is a fight, contraband found during a search, or any number of other incidents, the entire population gets locked down regardless of individual involvement. Facilities do not owe an explanation to inmates or their families, and most of the time none is given. Four to five days without showers during an extended lockdown is miserable but it is not uncommon.
From the outside there is genuinely very little you can do. You can call the facility and ask to speak with a supervisor or the warden's office, but do not expect much. You can contact the state department of corrections and file a complaint, which creates a paper trail even if it produces no immediate result. If the conditions are severe enough and persistent enough, a civil rights attorney who handles prisoner rights cases is worth a call, though that is a longer road.
For your inmate on the inside, the only real path through it is to keep their head down and endure it. Getting caught up in whatever caused the lockdown, or reacting in a way that draws attention, only makes a bad situation worse and potentially longer.
Nobody goes through something like this and thinks they want to come back. That feeling is worth holding onto.