Going to second Julian’s guess that there’s air in the system. And the volume of sound generated suggests the same conclusion. There may also be porosity in your print. The piezo disc may be leaking air where it attaches to the pump body.
Here’s a similar way to move water. Maybe less noisy.
If you’re going to pursue this angle, and you’re going to 3D print the device, you can also look into using a Tesla valve instead of “HSBB”.
On a pragmatic note, you can buy peristaltic pumps, some very small and suitable for microfluidics. These are metering pumps which may be useful for your application.