Modern transport category aircraft have redundancy in fire detection (especially engine fire detection)... both to ensure that a fire is detected if present, but also to vastly minimize the odds of a false alarm (especially engines).
If you get an engine fire alarm, follow the published procedure. OEI is not an actual emergency in transport aircraft, it's an abnormal, although you will declare an emergency with ATC to get priority handling.
If the second engine were to fail later, you could always restart the one you had shut down.