Round circle that stays while using the brush adjustment

when I am making other adjustments besides the first one.

I am not really understanding your problem from your description. Perhaps the following will help understanding.

(We are not talking about the "Spot Healing Brush" )

The Local Adjustment Brush will 'paint' adjustments on an area that you can visualize by turning on the Mask Overlay

The Brush only ever shows as two concentric circles-  Inner circle=Size { [  / ] }, outer circle=Feather {  Shift+[ / ] }

A "New" Brush can be started by clicking [Done] and clicking the Brush icon again- or simply pressing twice.  { K K }

Each brush leaves one pin- a small circle. The "Active" brush that will modify the image is indicated by the black dot in the small circle. Hover the mouse cursor on a pin and the Mask Overlay for that pin will become visible. Click any pin to make it the 'Active' Brush 

All the PINS (or only one selected) can be made visible or invisible with the options on the Toolbar (beside the Overlay option).

toggles the option Hidden / Visible

[Command+H] may not be a valid keyboard shortcut and simply does the same as

My method is to set the Brush pins to "Auto" and move the cursor off the image window to see the image without pins.