Hello! ^_^
I would probably say something like that:
虽然我不喝牛奶,我也吃牛奶制成的酸奶。
Although I don't drink milk, I do eat yogurt which is made of milk.
To describe a property of "yogurt", we just need to use a 的-proposition. The particle 的 is used to attribute qualities to things. You can use it to replace "that", "which", "who", etc.
Let's take a look at another example to see how it works:
这是我吃过最好吃的冰淇淋。
Zhè shì wǒ chīguò zuì hǎochī de bīngqilín
“This is the best ice-cream that I've ever eaten.”
Hope this helps!