Is there someone your son can stay with while you do this? That way if there is any threat to your health you can call a taxi to take you to A&E.
Quite frankly, if you are going through a divorce your ex is far more likely to mention your drinking than your doctor is. And if your drinking is being spoken of in the past tense all the better. I hate to say this, but your childs welfare should be up there on the list of priorities above protecting yourself from others finding out about your drinking.
Noone here wants you to carry on drinking, or criticise, but detoxing can be serious. If you were very poorly, say with sickness and flu, who would look after your child then? It might be the time to call them and say you are ill. It's not far from the truth. But your child waking up and finding you suffering is really not fair on them, and is likely something you would add to your catalogue of regrets. It is best avoided if at all possible.
BB