Yes, they are responsible, but I don't see where that gets you. It certainly does not provide a defense to the drunk driving charge. Unless your medical condition was aggravated by the delay, I'm not sure what your damages would be on a civil claim.
This answer is provided for general information only. No legal advice can be given without a consult as to the specifics of the case.
The police may be liable, but it is difficult to win and you typically must establish permanent injuries. I would start by seeing your physician immediately to determine the extent of your injury. You must start by filing a notice of claim, if you have one, and filing it on the designated party. Keep track of your symptoms and keep a journal of the date and time of the incident and other relevant information.
This is not intended as legal advice. It is only provided for educational purposes and cannot be relied upon as legal advice. Further no attorney client relationship is or has been formed by answering this question.
This question is posted ubder DWI. Perhaps it is more appropriate to repost it under the personal injury section. I don't believe the lack of medical attention will impact the ultimate question as to whether you were operating a motor vehicle while under the influence of alcohol or drugs, You should contact both an experienced dwi and personal injury attorney.