When you make changes to DNS entry of your domain or changed name server, it can take several hours to propagate across different DNS servers around the world. This is because each DNS server have its own cache, they only check for new DNS records when the record expire.
If you can plan in advance, set expire value for your DNS to lower like 1 hour before you make changes to your DNS entry, so your DNS entry will get expired in 1 hour and DNS servers update cache with new value.
Here are some useful sites to see which IP your domain resolve from different part of the world.
This site allows you to query different DNS records of a domain.
This site only ping to IP. That is you can check A record, not any other DNS records. This site can check from more locations.
DNS Propagation Checker in this site allows you to query A record from few different countries.