Checking for Local IP Address in C#
How the things will be?
1.Get the host name first by Dns.GetHostName();
2. Save the IP address in IPHostEntry by Dns.GetHostByName(hostName);
3. Using IPAddress array, get the actual host address.
4. Using IPAddress array, get the host address of local.
5. Compare the results of step 3 and 4.

For example, we are getting our local host and sending for the check.
You can check with the other remote IPs also by passing remote host while calling the bool method.
using System;
using System.Net;

public class ForgetCode
{
    static string IPHost;
    public static void Main()
    {
        UseDNS();
    }

    public static void UseDNS()
    {
        string hostName = Dns.GetHostName();
        IPHostEntry local = Dns.GetHostByName(hostName);
        
        foreach (IPAddress ipaddress in local.AddressList)
        {
            IPHost = ipaddress.ToString();
        }

        if (isLocal(IPHost))
        {
            Console.WriteLine("Yes, it is a local system");
        }
        else
        {
            Console.WriteLine("No, it is not a local system"); 
        }

    }

    public static bool isLocal(string host)
    {
        try
        {
            IPAddress[] hostIPs = Dns.GetHostAddresses(host);
            // get local IP addresses
            IPAddress[] localIPs = Dns.GetHostAddresses(Dns.GetHostName());

            // test if any host IP equals to any local IP or to localhost
            foreach (IPAddress hostIP in hostIPs)
            {
                // is localhost
                if (IPAddress.IsLoopback(hostIP)) return true;
                // is local address
                foreach (IPAddress localIP in localIPs)
                {
                    if (hostIP.Equals(localIP)) return true;
                }
            }
        }
        catch { }
        return false;
    }
}


If it is a local IP address then the output will be
Yes, it is a local system