It is always great when Scripture supports our work, especially in Pastoral Care. Take the Epistle reading for Proper 21, Year B, where we get James 5:13 saying,
Are any among you sick? They should call for the elders of the church and have them pray over them, anointing them with oil in the name of the Lord.
This isn't just a reminder for pastors to go and visit the sick. It is a reminder to us that when we are sick, we should let our pastors know so they can come visit us.
The great thing too is that if you tell your pastor directly, no one else has to know. Your pastor is under confidentiality, so the only way anyone else in your community will know you are sick is if you give your pastor permission to tell them.
Letting your pastor know directly when you are in the hospital helps your pastor help you. Plus it's in the Bible.