Castiel nodded. "I will go with you. If that's alright, Sam." Cas didn't plan to fade out unless Sam or Lydia asked him to. To Cas there was nothing strange about Sam taking two unrelated people to the doctor with him. That wasn't where his concern lay.
He turned to Lydia. "Close could be significant. Or it could mean nothing. It is a clue if that's where it started." He frowned a little. "I know you lost time but is there anything you can recall that stuck in your mind? Something strange? Something else strange?" Cas understood her frustration. In some ways he shared it. He didn't like fumbling in the dark any more than the humans before him. It wasn't at all what he was used to. He was created to be certain.
"When are we seeing the doctor?" Cas asked, walking around the room slowly, wondering if it would help him think as it helped Dean think.