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That's common in people with lactose intolerance. Yogurt is cultured with bacteria and the first thing the bacteria eat up is the lactose because the sugars are the easiest for them to digest, so there's little to no lactose in yogurt. I'm not as well versed on cheese making, but I think they often use bacteria cultures in the processing, so that would also eat up the lactose.
I'm lactose intolerant, too. Milk and ice cream are full of lactose, so when I remember, I take a dairy digestive supplement before eating them and I feel great. Everyone naturally loses the enzymes over time because we're the only mammels that continue to drink milk after infancy. Some people lose the enzymes early and some people lose them later, but most everyone will lose them. I started showing signs of lactose intolerance in my early teens but one of my college profs (who taught all this) said he didn't start showing signs until his early 60's.
To answer your original post - I've never tried almond milk. I'm the same way as you - I can eat yogurt and I love cheese, but I can't eat ice cream (don't like drinking milk anyway.) I suggest you try using dairy digestive supplements or trying some Lactaid milk before you give up on milk and ice cream.