In order to speak about illness, sickness, diseases, you need the appropriate vocabulary.
Asthma - an illness which makes it difficult to breathe;

Bronchitis - an illness in your lungs which makes you cough and have problems breathing;

Influenza - flu (= an illness like a very bad cold, that makes you feel hot and weak);

Stroke - a sudden problem in your brain that changes the flow of blood and makes you unable to move parts of your body;

To break one's leg/arm - to damage a bone in your leg/arm, etc;

Abscess - a painful, swollen area on the body which contains a yellow liquid;

Cold - a common illness which makes you sneeze and makes your nose produce liquid;

Incurable illness/disease - sickness that is impossible to cure;

Poison - a substance that can make you ill or kill you if you eat or drink it;

Fracture - to break something hard such as a bone, or a piece of rock;

Cut - to injure yourself on a sharp object which makes you bleed;

Pimple - a small spot on your skin;

Cancer - a serious disease that is caused when cells in the body grow in a way that is uncontrolled and not normal;

Heart attack - when someone's heart suddenly stops working correctly, sometimes causing death;

Bruise - a dark area on your skin where you have been hurt;

Sunstroke - an illness caused by spending too much time in the sun;

Rash, (skin) eruption - a group of small, red spots on the skin;

Epidemic - when a large number of people get the same disease over the same period of time;

Ulcer - a painful, infected area on your skin or inside your body.

She had an asthma attack.

Carolyn broke her leg in a skiing accident.

He caught a bad cold at school.

She cut her finger on a broken glass.

I think he's had a heart attack.