Why can’t I eat ice cream or drink milkshakes?

Have you read and written down the ingredients on the ice cream you buy (you can ask to see what goes into a milkshake) and compared them with the list of ingredients in yogurt and some cheeses? Because the ice cream can contain thickening agents, artificial flavors, other chemical compounds that aren't present in milk and butter, and might not be found in the cheese and yogurt you eat.

Where the problem seems to stem from eating ice cream in both cases, it may be an additive in the ice cream that is causing the issue. Have you googled the ingredients typically found in the ice cream to see if there may be something there that can cause a gastric issue?

PERHAPS ITS THE FLAVORINGS IN THE ICE CREAM OR MILKSHAKES?.

Most ice cream isn't 'just' milk. Most commercial ice creams contain other chemicals and preservatives to maintain the texture. You could be reacting to one of those chemicals.

Try vegan milkshakes.

Thinking out loud here.

The gas from the ice cream, which is also in milkshakes, may be causing your internal bacterial flora to get agitated. They produce more gases which leads to pain and diarrhea.

You may be suffering from bloat. If you research further, bloat can also be caused by a good number of healthy foods including bread and vegetables. To get better answers to your problem, it would be best to ditch google and ask a doctor instead.

This is a response to curtisports2. Thanks for your answer. I seem to be unable to post a comment under yours, for some reason! No, I can’t say that I have written down ingredients in the ice cream I have eaten, but it seems to make no difference which brand. The result is the same. It makes no difference where I buy the milkshake, same results. What you said about thickening agents is interesting. You may have hit on the answer I need. I never thought about that possibility. That might successfully narrow down a google search.