How can I accurately measure glucose concentration in culture media?
The most common method of measuring glucose concentrations (in pretty much any sample) is an enzymatic assay based on the glucose oxidase enzyme. This method is reliable because the enzyme is known to be quite specific for glucose; it does not oxidize fructose, galactose, or any of the other common hexose sugars which can contaminate many other measurement methods. The enzyme can be coupled to other reactions so that the amount of glucose oxidized can be read out by a standard spectrophotometer. There are many kits commercially available based on this principle, like this one. A review of glucose oxidase from the glucose measurement perspective is found here.

Blood glucose analyzers are also based on glucose oxidase. Typically, they have disposable slips that contain glucose oxidase along with some electron-carrying chemicals that convert enzyme activity into an electrical current sensed by the device. It is possible to measure glucose in pretty much any solution with such insruments, but as mentioned in comments, you need to make a calibration curve for glucose in your solution of interest (culture medium, or whatever), as you cannot trust the readings from the instrument directly when measuring under different conditions. We have previously used this approach to measure glucose in mammalian cell culture medium, and it works fine in our hands.

It is also possible to quantify glucose by mass spectrometry or nucleic magnetic resonance methods, but unless you have such a facility and expert help, I guess that is not an option in this case.