There is no actual "standard" way to find out if that person has blocked you, but there are some cheeky hacks and third-party apps you can use to find out.
One option is to simply create a new Instagram account and then simply use the "Search" function to see if that person’s profile comes up. If it does, then it is almost certain they have blocked you.
InstaFollow is an app that helps you manage your Instagram account and track your followers. You can view who's followed and unfollowed you on here.
StatusBrew also allows you to easily manage your social media accounts.
Download the app, login using your Instagram account then click on your Instagram Account. Click on "New Unfollowers" tab on the left sidebar.
You’ll then need to pop to your Instagram app and search for the names of the people who have unfollowed you from the list.
If you cannot find their profiles, it means you've been blocked and you will have to fiend a new pal to make up your numbers!
Go find out who your frenemies really are ...