While the caring and knowledgeable attorneys of Avvo can provide accurate information about the law and legal procedure, this Q&A is ill-suited to advising strategy in a specific case. You need the representation of experienced criminal defense counsel before you cause additional problems for yourself. Retain counsel or apply for the public defender, and do so before engaging further with the police.
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This answer is offered as a public service for general information only and may not be relied upon as legal advice.
If you are prosecuted and the State wants to use your statement as evidence against you, then your lawyer would consider filing a motion to suppress the statement on the grounds that it was involuntary. The judge would hold a hearing on the motion at which you, the officers, and any other important witness to the statement, would testify. Depending on what the testimony at the hearing reveals, the judge would either grant or deny your motion to suppress.
You should absolutely get yourself an experienced criminal defense attorney right away. Do not talk with the police or sign anything they give you without your lawyer present.