My 6 Year Old Had Blood Drawn Today My Other

My 6 year old had blood drawn today my other child is currently sick with a cold virus. After my 6 year old had blood drawn she has had fever. We took her to the doctor they gave her antibiotics because the doctor said my other daughter probably got her sick. But my question is my daughter who had blood drawn keeps getting fever did having blood drawn causing the fever to keep coming back...we did not know she was getting sick when she was getting her blood drawn