Is it true that you can infect your heart while having tonsillitis?

Rheumatic fever is an infection of the heart valve (which can damage the valve) which can occur in someone with strep throat tonsillitis (or possibly with other types of bacterial tonsillitis, but it is rare when a person is treated with appropriate antibiotics for the strep throat. That is likely what you are thinking of

What happens with strep infections is that your body make antibodies to fight these infections. The strep bugs look very similar to the your heart valves, immunologically speaking. The antibodies that you make for the strep then attack your heart valves and your heart valve suffer with damage. This is called rheumatic heart disease. We don't see if very often because we have antibiotics.