I have a temperature sensor connected to Arduino MEGA 2560 R3, where I have attached a SIM 7600 CE-T 4G module. How can I display the sensor's readings via the use of 4G module to my laptop, either on the Chrome browser or any better way, but without the use of a 3rd party website...
Use GPRS to establish an internet connection through the cellular network.
The 'client' side needs to find the IP address of the 'server' side.
You can set your laptop up with Dynamic DNS to assign a name to the laptop's address. That will make it relatively easy for the SIM card to get the address.
If your laptop is on a private LAN (most are) you will need to set up port forwarding in the router to allow a connection from the Internet to a port on your laptop.