You should talk to a lawyer in your area about your defense. It may be possible to withdraw your uncounseled plea.
This response is for informational purposes only and is not offered as legal advice.
Withdrawing a plea can be an uphill battle. But it is much easier before sentencing than it is after, especially if you have not had the assistance of counsel yet.
When asking the court to withdraw your plea, I suggest you NOT go in to the facts you posted. Just advise the court you have not had the benefit of counsel and would now like to consult with an attorney.
Quite frankly, the defense the police somehow entrapped you into driving is not very convincing. For entrapment to work, you must have no other opton. You could have called a cab or the police. You could have kept calling others until you got a ride. You could have walked away. (Although, the freezing weather conditions do make entrapment somewhat more viable...)
Maybe a necessity defense? But even for necessity, you still had to have no other option.
For more specific advice, consult directly with DUI defense attorneys or the public defender's office. Do NOT post any more details regarding your case online. The more you post online, the less confidential your case becomes. Also, anything posted online may be used against you in court.