There are two main sensor types for current, Shunt Resistor - is installed in series, that is inline with the current path, the other is a Current Transformer ( or a related Hall Effect) - there are others. Since both of these require you to access the individual cables (conductors) of the Mains ( residential feed) - it is a job for a proerly qualified individual. Also note - to combat theft of electricity the actual electrical meters ( external ) are pretty hardened, making it nearly impossible to measure these values "at the meter", you can not walk up to the meter and get this data..
These are JUST the sensor - you then need an instrument to interpret the signal and provide you with the data as you have asked for it. For example a sensor does not tell you "how it looks"... that is the instrument's job.
Based on your language - it seems you are suspecting the utility, or the meter itself to be at fault