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The inductor does several complicated things. To grasp the relationship between voltage and current...

It may be easier to imagine the inductor operating in propulsive mode. That is, at a moment when the flux field has built and current is flowing.

Quickly attach an ohmic resistance across the ends but no voltage source is attached. Call the time t=0. The inductor generates voltage, sending current through the resistance around a loop.

Now the above setup serves as a tutorial to see how inductive reactance works. Time constant is LR. Convention agrees that the characteristic behavior lasts for 5 time constants. Ampere level immediately is at a peak, then declines on a familiar curve. Volt level likewise immediately starts at a peak, then declines on a familiar curve.