Can someone have a really bad infection from a wound and feel fine but it reaches their heart and kills them without them having warning signs?

Endocarditis: If you have a normal heart, it is unlikely. If you have heart valvular abnormalities and certain kind of bacteria get into the blood stream from a wound, it is possible, though rare. More commonly endocarditis occurs in IV drug abusers.

No signs is unlikely: If an infective agent travels to the blood stream and spreads, it could cause what is called sepsis. With sepsis the body is greatly challenged to fight the infection. In severe cases the patient may go into multi-organ failure, shock, or even death. Have it evaluated and get the appropriate treatment.