Rose smiles and slowly falls into a light sleep so that if anything happened and she was needed she wouldn't be groggy. 
Gwen came into the TARDIS feeling a little odd about entering a person's home, carrying the tea, while Owen came in with the medicine in a shot knowing the Time Lord wouldn't be able to take it. 
"I didn't put anything in it as I wasn't sure how you took it but Ianto said to just trust him, and seeing as he does this the best I am not arguing." Gwen says with a warm smile to the Doctor. He was part of the reason she had such an interesting job. Owen went to the Doctor, wiping his arm down. 
"This will sting a bit." The human doctor warned giving the shot expertly. At least he was honest about these sort of things instead of the normal 'this won't hurt a bit' BS other human doctors said.