When making changes to DNS there is always a period of doubt where the TTL hasn't expired and your changes haven't fully propagated.
There are a handful of tools online that can be used to detect how the propagation is going: https://www.whatsmydns.net/ is one of many sites designed specifically for that task.
However there is a built-in command line application in most Operating Systems (Windows, MAC OSX, and Linux) that you can use to connect with external DNS servers and check what they are seeing when you query them about your domain.
The app is called nslookup and to get to you must use the command line. In Microsoft Windows you can do that by searching for run at the start menu - or by pressing the windows key and the letter R. This will display the run command input box.
As Above - type in cmd and hit enter or click OK.
*Type in and hit enter: nslookup
*Type in the domain you are looking for and hit enter: example.com
This shows the results of the default DNS server for your computer.
A good test is to see what the Google public DNS knows about your domain - to do that we need to change the server we are querying.
*Type in and hit enter: server 220.127.116.11
As you did in the previous step type in the domain you want to check and hit enter.
This shows us what Googles public DNS knows about the domain in question - as you can see from the images above - there are no differences shown - so the DNS is up to date for this example.
To quit out of nslookup just type quit and hit enter: