最佳答案应该是 from：

He was becoming quite ill from the smoke, and I had to take him out of the room. 他被烟味弄得很难受，所以我要带他离开房间。

表示患有某种疾病，常用be ill with；表示因某种原因而生病或难度等，通常用be ill from。

be ill with 的例句

She fell ill with flu. 她患感冒，病倒了。

Samantha was seriously ill with a fever. 萨曼莎烧得很重。

Unde Harry is terminally ill with cancer. 哈里叔叔的癌症已到了晚期。

Mother became seriously ill with pneumonia. 母亲得了肺炎，病得很重。

be ill from 的例句

Last week she fell ill from cold. 上星期她着凉生病了。

Even my mother became ill from anxiety. 连我母亲也急出病来了。

He’s ill from want of sleep. 他因睡眠不足生病了。

He fell ill from eating unclean food. 他因吃了不洁食物而生了病。

但以上区别也不是绝对的，比如有时也用 with 来表示原因。如：

She felt ill with / from exhaustion. 她过度劳累，终于病了。

She was making herself ill with worry. 她愁得生病了。

Robyn was almost ill with excitement and outrage. 罗宾情绪激动，一气之下差点儿病倒。