Easiest things first. Change mice/try a trackpad. I suspect a sticky mouse button, or maybe enough dirt on the contacts that the OS 'thinks' it's still pressed, even when you release it.
Oh! I still use a wired mouse, but you probably have a wireless/blue tooth mouse? How well charged are its batteries?
Even if you are using a mouse, check Accessibility->Mouse & Trackpad->Trackpad Options->Enable dragging->
without drag lock/
with drag lock/
three finger drag.
Also check Accessibility->Keyboard->Sticky Keys. There may be a key selected that and it may be stuck down.
Finally, check Accessibility->Switch Control->General. Is "Enable Switch Control" checked? BTW, I have no idea what "Switch Control" is used for.
If you have OnyX, Cocktail, etc. go through all their options/tools/functions to see if any of them affect the mouse buttons.