Is it permissible to take out a loan that is Islamically forbidden in order to treat a sick child whose treatment is not available locally, and whose health condition is deteriorating day by day?

If a person cannot find a permissible means to treat his son, then it is permissible for him to take a prohibited loan out of necessity, which is saving a life on the verge of perishing, as Allah Almighty says: "And He has elaborated for you what He has forbidden to you, except what you are compelled to [eat or do]."