Strictly speaking, Kirchoff's circuit laws are not valid in AC circuits. However they are often good enough for engineering work.
That in turn means that the change in current causes a change in the magnetic field, which is manifested within the electric potential. I realize the potential is still defined and thus a line integral over a crossed curve of ALL of it's component should be zero.
The first thing you should have been taught about Kirchoff's laws is that they are valid for lumped circuits. This means the laws are an approximation that is valid when the circuit can be approximated by an idealized lumped circuit model.
The lumped circuit approximation requires that the circuit be small relative to the wavelength associated with the highest frequency signals to be modeled in the circuit. In engineering we usually take this to mean that the largest dimension of the circuit is less than 1/10 of the shortest important wavelength.
The lumped approximation allows us to neglect the magnetic flux through the surface enclosed by the circuit (so that KVL is valid). And it allows us to neglect charge accumulating in the wires connecting the circuit elements (so that KCL is valid).
Of course inside individual components of the circuit (inductors and capacitors) there can be significant magnetic flux or accumulated charge. But we model that by the consitutive relations for those elements. What we neglect is the magnetic flux and charge storage on the wires between the elements.