Hi, let me help you.
Do you have a spare USB mouse or a Bluetooth mouse?
Plug in a USB mouse (or use a Bluetooth one) and see whether you regain control during an episode. If you do, and the chaos continues without you touching anything, then disable the touchpad in Device Manager (right-click Start, open Device Manager, look under Mice and other pointing devices) and see if the problem stops. Let me know the result.
After that, run the Dell Diagnostics. Restart, tap F12 repeatedly as soon as the Dell logo appears, and pick Diagnostics from the boot menu. Please let me know if you see any hardware test error messages.