Everyone has facial asymmetry, but like you wrote, you may be noticing it more as you get older. Fillers can help balance them a bit better. But I try not to go for exact symmetry, but rather improvement for each side of the face.
There are many aspects to facial asymmetry. One needs to evaluate the facial boney structure, the muscle activity, One side of your face show more hyperactive muscles. The volume and distribution of fat, one side is different than the other. Brow position and upper lid are different.
Some aspects of the asymmetry can be improved, however the bone and muscle action asymmetry can not be changed. A personal evaluation to evaluate the face in the static and dynamic aspects of the face is needed.