1. 다치진 않았어요 = 다치지는 않았어요
the ~는/은 attached to “~지” in that sentence is used to compare something.
It almost always is compared to “one’s expectations.”
For example,
그것은 쉽지 않다. = It is not easy.
그것은 쉽지는 않다. = (despite what you expect,) it is not easy.
다치진 않았어요 means "(despite what I expect,) I'm not injured.
2. 퇴원하셔야죠
퇴원하셔야죠 is honorific expression of 퇴원해야지
퇴원하셔야죠 << 퇴원하(다) + 시 + 어 + 야지 + 요
퇴원하다 : to leave a hospital
시 : honorific suffix indicating the subject person is elder than the speaker
Verb + 아/어/여 + 야지 : This pattern is used to indicate obligation, but it is stronger and insistent than the grammar patterns V + 아/어 + 야 되다 and V + 아/어 + 야 하다. It is often used as a response to something obvious or said when the other person knows something must be done. When used as a response this pattern is approximately equal to '(Of cource) I have to' ~ or '(Of course) I must ~' in English.
요 : honorific ending suffix