01 Jetta Overheating, possibly fan?

Hello,
We have a 01 Jetta with 144k miles. Normally, the temp gauge is at
190 deg. It is marked with hash marks up to the red mark in 17.5 deg
increments, the red mark is at 260 degrees F.
At present, it goes up to 245 degrees at which time I turn the car
off.

When I open the coolant reservoir, a slight pressure release is heard
adn teh reservoir fills up to about 3/4 inch more.

At the 245 degree point, the small van is running and the larger fan
is not.

My presumption is it might be the fan or a control module.

Any way to test which or am I heading in the wrong direction?

Thanks for any help, can't afford a repair shop just now,

Dermott