It sounds like the breaker is doing exactly what it is there for; tripping
in response to an overload.
I doubt it is defective because then it would probably trip without getting
hot; but if you want to make sure, you can swap two breakers and see what
happens. If the problem goes with the breaker, it is defective. If it
stays with the circuit, it is an overload.
However, in the interest of being conservative, you should probably turn the
breaker off, and carefully see what doesn't work anymore. Odds are, you
will find something big that you didn't know was on that circuit.