you should have gotten an auto save prompt there O: there is a chase, but if youre worried about getting through that part ill give you some tips!
make sure you took the pain medicine in your inventory (this will increase your walk speed to normal if you havent done so), be right to the left of the trail of blood leading up (this will place you in front of the door so you should be able to just press up and run out faster), head to the second floor (NOT the first) and then go across the board and to the lobby, go across the lobby and into the original part of the hospital, do NOT use the elevator and head to the stairs! that should get you past the chase!
you cant save from menu btw, but if you saved at the prompt youll reload from there