So I have a few brushes in PSD file format, but when I try to append them into Blender they don't show up.
To import brushes in blender, you would have to convert it to jpg or png first. You can do it using GIMP. Open GIMP, drag and drop the PSD file and export it as jpg or png.
Also, appending them wouldn't work since it is not a .blend file. You would have to import them. Open user preferences, add-ons and search for 'Import Brushes'. Activate it and from the file menu, select Import, 'Brush Set' and browse to where you have saved your file.