DIAGNOSIS The impact likely cracked the trigger housing internally or dislodged the trigger's return spring. A loose trigger that self-activates is a serious safety issue.
FIX You need to open up the drill. This means removing the housing screws. 1) Remove the battery. 2) Take out all the visible screws holding the two halves of the main body together. 3) Gently separate the clamshell. You'll see the trigger assembly mounted to the inside. 4) Check if the plastic trigger piece is broken or if the small metal return spring has popped off its post. If the spring is off, just re-seat it. If the plastic is cracked, the trigger needs replacement.
IF THAT DIDN'T WORK If the trigger looks intact and the spring is in place, the drop may have damaged the electronic switch module the trigger presses. This is a soldered circuit board component. At that point, for most people, it's a warranty or service center job, as replacing the switch requires soldering skills.
HEADS UP Until this is fixed, treat the tool as live and dangerous. Do not install a battery. A runaway drill can cause injury or damage. If you're not confident opening it up, this is absolutely a case for sending it to Milwaukee for repair. Don't tape the trigger down or try other workarounds.