I would consult an experienced immigration attorney.
Ice might have already put a hold on you- or they might still do so. You might get lucky and nothing happens. At this time, the jail should be able to tell you if there is a hold on you- but that has nothing to do with what they might do in the future.
There is a presumption in immigration law against admitting people who are alcoholics, and so even if there is no hold placed on you at this time, you could have trouble re-entering the country at a future time. You could have trouble the next time you renew your green card, and you could also run into trouble when you apply for citizenship.