As frequency goes up so does inductive impedance. Or are you asking if the inductance itself changes with frequency? The answer to that should be a no.
Amending my earlier statement, apparently inductance can rise with frequency but is application dependent. It does not appear to be an issue at audio frequencies. Here is the reference...
Kenneth Lundgren
, M.S. Electrical and Electronics Engineering, Northwestern University
Answered September 8, 2017 · Author has 6.5K answers and 2.5M answer views
All the answers here except Roy MaCammon’s ignore what the OP has asked. All of the math about the reactance increasing with frequency is true. However, every inductor has a self-resonant frequency which is caused by the stray capacitance within the inductor. At the self-resonant frequency, the reactance will be much higher than predicted by X=jωL. So as the frequency approaches the resonant frequency, the equivalent value of L will actually increase. In a high Q inductor, L may appear infinite.
At frequencies above the resonant frequency, the inductance will actually appear negative, i.e. capacitive.
INDUCTOR IMPEDANCE vs FREQUENCY:
APPARENT INDUCTANCE vs FREQUENCY:
If the inductor is being used as a choke - to block high frequency AC, you can use this to advantage, by selecting an inductor with a resonant frequency close to the frequency that you want to block.
There are special inductor designs to maximize the self-resonant frequency by minimizing the self-capacitance.
There may be several self-resonant frequencies.