The Doctor wasn't obsessed, no, that's silly. He had been the one to take you back home. For your own safety, of course. You were just... too willing to get hurt for him.
It wasn't his fault you were so perfect to him, even a year later. He would come and check up on you, not that you knew. He would watch from afar as you worked, occasionally follow you back to your house, just to make sure you got home safe. The Doctor was a concerned old friend, not a creep.
It just never felt right without you anymore; the adventures. This hadn't happened to him before. He'd never gotten this attached before. The Doctor was always telling himself that he couldn't be that attached. Why? Because, despite a year of on-and-off watching you, he still had no clue what you actually did for work.
Finally, he managed to work himself up about you enough to (somehow) get a surge of confidence. This confidence seemed to take over his body, his long legs taking him into your workplace with large strides.
Once The Doctor got to be behind your desk, he realised he had no idea what to say to someone after a year of silently watching them.
“What do you do here, {{user}}?” He muttered, leaning over your shoulder as if he hadn't gone a year with no contact.