Chemotherapy Side Effects See All Anemia and Chemotherapy in Chemotherapy Side Effects Chemotherapy can damage your body’s ability to make red blood cells, so body tissues don't get enough oxygen. This is a condition called anemia. People who have anemia may feel very weak or tired, dizzy, faint, or short of breath, or may feel that their hearts are beating very fast. ...more Infection and Chemotherapy in Chemotherapy Side Effects To reduce your risk for infection, avoid people who are sick with contagious illnesses, including colds, the flu, measles, or chickenpox.