The phrase 'got sick with' is correct and usable in written English.
You can use it when talking about becoming ill with an illness. For example, "My friend got sick with the flu last week."
Then I got sick with encephalitis.
Then one of the nurses got sick with Ebola and died.
In the Russian camps, people got sick with scurvy, from a lack of vitamins.
New Orleans got sick with Katrina because of the artificial, unnatural acts of man stretching back over a hundred years.
In addition I also got sick with loin pain," says Dakheel, speaking to the Guardian through a translator.
There were blizzards in northern England barely a month ago, and Rebanks's sheep got sick with pneumonia and fluke.
Each day he got sicker, with a dry cough, night sweats, nausea and vomiting, shortness of breath.
MORE than eight million people get sick with tuberculosis every year, according to the World Health Organization.
Frankie gets sick with headaches sometimes and Johnnie brings him soup and cigarettes.
