Is this your first time unlocking/flashing a device? If it is, I would recommend first looking into installing the android adb tools, sometimes you can find minimal installs, then turning your phone in boot mode and trying to comunicate with it. This is usually done with the terminal and after you send a specific command the phone should reply with its identifier (i dont remember the specifics). Once you can communicate with the device this means the drivers you need are installed properly and you should be able to see your phone in the xiaomi application (or unlock the bootloader directly from the terminal).

All of this assumes you got the unlock code from the xiaomi site (which ofently does not work) but there are some shady programs around to bypass this step.

Did you also installed the drivers? It took me some time to learn that your computer may see the phone in regular mode (accessing content) but not when you turn it on recovery mode / boot mode and this requires additional drivers.