表示“打点滴”或是“输液”，英语有个常用单词是 drip。其常见搭配是 be on a drip, put sb on a drip 等。如：

 She's been put on a drip. 她一直在输液。

He was on a drip for three days. 已经给他打了三天点滴了。

At the hospital they put me on a drip. 在医院，他们给我输液。

你的句子可以翻译成：

He has a cold and is on a drip.

Having a cold, he is on a drip.