Sirius needed to stay because if he left now, Teddy would have spiraled even more than he had. So once he had that touch back, he pulled to get Sirius off that chair and onto his bed. He could sacrifice the crawling of his skin if it meant he could convince Sirius not to tell anyone else.
"Harry doesn't know - I really hope anyway," Teddy murmured, "I just say I'm sick and that's the end of it. It's my own little code just to keep things normal," he trailed off for a moment. Then he shook his head and frowned to himself, "Tell me Padfoot stories."