Hi and welcome Peter.
In short probably not very good for you.
Have a read of the welcome pack here https://www.diabetes.co.uk/forum/threads/basic-information-for-newly-diagnosed-diabetics.26870/
Carbohydrates in whatever form aren't great for T2's... milkshakes are usually sweetened with sugar and if they contain milk with lactose then that's another carb so they are a double "bad" whammy.