Here is what happens in real life ... the police will NOT give you your medication. They MIGHT bring it with them to the jail and hand it over to the jail staff. Unless your medical need is an injury or life threatening, they are not going to haul you to a hospital because of a possible mental health issue.
Once at the jail, you will be subect to the policies and procedures of the facility. They also will NOT allow you to consume medication you bring in until (and unless) it is approved by their own medical staff. Generally, if you will be staying more than a day, they will write a new prescription if it is necessary. A public intoxication beef that will likely result in incarceration for far less than 24 hours will NOT result in a doctor's visit or prescription.
But, if you have the money, you can certainly pay an attorney to write letters, make a claim and try to sue the police or the jail for failing to feed you your psych meds in a timely manner. Good luck with that.

