How to calculate the total torque for a rod whose axis of rotation keeps changing due to external force

Suppose I have a rod of length L and mass M. I swing the rod by holding at one end. I need to compute the total torque acting on the rod if I know the position of the center of mass of the rod and the ends of the rod in 3D. I am using the torque equation below.
I have a setup where I can get the coordinates of the ends of the rod in a global coordinate system. The coordinates are provided at the rate of 120 Hz.

$$
T_A=C_A+M_A=I_text{cm}alpha+omegatimes(I_text{cm}omega)
$$

Because the rod is rotating should I calculate the $ I_{cm} $ at every rotated axis passing through the center of mass? In which reference frame should $ I_{cm} $ be calculated and in which $ omega $ should be calculated.

My method is as below.
Take an arbitrary axis the origin of which passes through the center of mass of the rod.

Calculate the inertia tensor about the above decided axes. Calculate the angular velocity of the body in the global coordinate system. Calculate the angular acceleration in the global coordinate system.
Use the equation above to calculate the torque.
Repeat the above two steps for each new position and orientation of the body.

After every rotation the inertia tensor will change. The angular velocity and acceleration may also change and will recalculation.
Any thoughts, ideas, discussions are most welcome.