Perhaps measuring works better if you give the servo more to do. Then the time there is for measuring is greater. And because you do not measure and print 360 times in the loop() the program will be faster.
There's a bad current flowing into your Arduino, if ADC voltage exceeds Vcc (5V). This undesired current can be limited by a resistor. But if there's such a high voltage across a shunt resistor, something else is wrong. You rather suffer from a too small voltage for useful measurement.
My first doubt is rather, whether it's safe for the shunt resistor.
Let's imagine that you expect to have 1A of current going through your circuit.
Resistor of 0.1 Ohm will give you a voltage drop of 0.1V.
This causes two problems.
Firstly Arduino has a cheap ADC builtin. It's supposed to be easy to use, but not really precise. It has nonlinearities towards lower and higher range. You will get more precise reading when ...