When House's heart stops, Wilson and Cuddy perform CPR on him, with Cuddy doing mouth-to-mouth resuscitation. However, she is doing it incorrectly; she is not pinching his nostrils shut, which is necessary, otherwise the breath of air will escape out of the nose, making mouth-to-mouth ineffective.
There is no way a doctor (even Cuddy as House would say) would tell someone with a head injury to go home and go to sleep. That is incredibly dangerous, as the victim could easily lose consciousness and possibly even die due to worsening of their intracranial pressure, plus House has taken enough opiates in one go to cause respiratory depression and possibly respiratory arrest.
When the stripper finds out that House has a hole in his head, she is unaware of the accident outside and that he may be.a part of it based on his forgetfulness and manner of speaking. It is extremely unlikely that no one in the strip club is aware of such a huge accident and not informed others of it.