Typically, the determination of whether a sentence is served in jail or on EHM is made at the plea/sentencing hearing by the judge or is incorporated into the deal as part of the negotiated plea bargain. If EHM was not agreed to as part of the plea agreement or if the judge heard your request for EHM at the sentencing hearing and denied it, there is not much you can do at this point. Consult with your attorney about this issue to get a more personal and case-specific answer.
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This is an issue that should be addressed by the judge at sentencing. It sounds like that may have already happened, so it may be too late. In some counties judges approve EHM on the sentencing order without drawing attention to it, sometimes as an option avaiable at the discretion of the workhouse or probation. You could check that. Otherwise it is unlikely to get changed.
As has been said, whether the sentence says EHM or work release is decided by the judge at the sentencing hearing. If you asked for EHM but were denied, it is unlikely the judge would change his mind.
It is technically possible for a judge to modify the sentence. Your lawyer could make a motion to modify conditions of sentence. Unfortunately, there is no guarantee this would work, and the judge could deny your request. Typically, your attorney would talk to the prosecutor first to see if he would agree. If both your attorney and the prosecutor agree to the switch, then the judge is much more likely to approve it.
As mentioned, you should talk to the lawyer who represented your original case, since (s)he knows the facts best.
Good luck to you.