火曜日に入院して、金曜日に退院するって英語でなんて言うの？

1. I'm going to the hospital on Tuesday and I'll be there until Friday.
   This is a direct statement that means exactly what it says.

2. I'll be admitted to the hospital on Tuesday and discharged on Friday.
   In English we use the verb "admitted" to describe someone who checks in at the hospital. We use the verb "discharged" to describe the action of checking out of the hospital.

Admitted to the hospital' = 入院する
'discharged (from the hospital)' = 退院する

When a patient visits the hospital with a medical problem, they will be examined by a doctor and either 'admitted' to the hospital, or sent home, perhaps after having received some treatment.
The patient may stay in the hospital for a short or protracted period of time before being 'discharged.'
"How long will you be in hospital?"
"I'm being admitted to the hospital on Tuesday and will be discharged on Friday."

When you are hospitalised you are ill/sick enough to go to hospital, therefore we say that a person has been 'hospitalised'. We use the words 'from' to indicate the start of the hospitalisation, and 'until' to denote the length of time spent in hospital. When someone is 'admitted' it means they have been told by a doctor that they need seek treatment at a hospital.

You could also say that you endured a hospital visit. This will prompt the person you are speaking with to ask how long you stayed. You may then specify that it was from Tuesday until Friday.

When we are permitted entry into hospital we call we you are 'admitted' to hospital and when we leave we are discharged.
We can use the sentences above to say that we are going to the hospital on Tuesday and will be back home on Friday.

Discharge: being checked out of the hospital to go home
Admitted: being checked into the hospital
Hospitalized: admitted to hospital