I read that if u have a chest infection u can't eat ice. Cream cus. It puts pressure on lungs. How that happens? Can I take cold drinks?

Who said? No truth to what you are saying in the question. When you are fighting infection, it's best to eat food with good nutritional values but if you want to eat ice cream or drink cold drinks, there is no reason why you can't.
Ice cream for lungs? There is no scientific basis to an assertion that ice cream puts pressure on the lungs. Ice cream/popsicles are commonly recommended for people with sore throats, just because it tends to numb the throat and reduce pain. In answer to your question, there is no reason at all why you cannot take cold drinks in the context of a chest infection.