Short to ground. Please help!

Side note:
Some multimeters have are capable of reading moderate current flow for short periods of time.
They will have a setting for 0-10 amps or something along those lines. They will typically have a fuse on that function.
Use this only when you are absolutely sure the current flow is less than the 10 amps or whatever it can handle.

Current is electrons moving. No movement = no current, therefore zero amperes.
Potential is electrons excited, looking to go somewhere. Voltage indicates energy level available at that location; either compared with ground, or another location if the second probe is someplace other than ground.

When there is a connection allowing a complete circuit the electrons move. Only then is there current flow. By accepted convention we describe this as current flowing from high voltage to the lower voltage.
A short is when the electrons find an easier, lower resistance path to back to ground.
An open is when there is a break in the circuit.

Your immediate problem with the turn signals is that there is a break in the feed line.
The cause may have been a short that caused the fuse to melt.