Diode selection for step-down Converter
In your case, I wonder whether your diode actually had a reverse current of 100 mA. That seems humongous.

Let's start from the bottom:

When currents become large, the forward voltage, even that of Schottky rectifiers, becomes a significant contributor to loss.

Thus, one usually uses synchronous switch mode power supplies:


  Someone told me I could use a transistor instead of a diode, but I have no idea about that; does it make sense?


Yes, it makes very much sense! You know exactly when that diode should be conducting, and when not. Instead of a diode, you could have another switch like the transistor feeding input voltage into your inductor.

Typically, MOSFETs (for medium currents, like yours) are  used, which can have excellent r_ds,on, meaning there's very low voltage drop.

You can buy, for your power regime, ICs that integrate both the high-side switch and the low side switch (examples, esp. this).