You could try to withdraw your guilty plea by filing a motion to withdraw your guilty plea in the court. It would be the court's decision whether to grant your motion and withdraw your guilty plea in your case. It is not easy to get this type of motion granted. I would advise hiring a criminal defense attorney to represent you in this case.
Juan C. Garcia, Jr.
GARCIA LAW OFFICE, LLC
A defendant's ability to withdraw his plea is largely dependent on the specific statements made at the time of the guilty plea. The Judge should have reviewed your Constitutional rights, which includes your right to a speedy public jury trial, right to cross-examine and confront witnesses, right to compel witnesses, and right to testify and privilege against self-incrimination. Almost always the court will require the defendant to sign a statement of defendant in support of guilty plea and certification of counsel, which contains an explanation of your rights.
These difficulties arose because you plead guilty to something you didn't do. You should never plead guilty to something you didn't do. Unfortunately, some of my fellow criminal defense attorneys are scared of taking cases to trial. You need to hire an attorney who is willing to fight for you and take your case to trial.
If you have not been sentenced, you need to file a motion to withdraw your guilty plea and convince the judge to allow the withdrawal. It would not necessarily be granted automatically, just because you asked for it. You need to demonstrate to the judge why it should be allowed.
If you have been sentenced, then it is likely too late to withdraw your plea. If you are in the district court in Utah, you will likely need to look into finding an attorney to do some kind of post-conviction relief work for you.
If you are in one of Utah's "justice courts" (courts where there is no verbatim record kept of proceedings) and have been sentenced, then the best option would probably be to hire an attorney to file a notice of appeal for you. You have the right to an appeal from justice court to district court.