Snapchat will not notify you when someone blocks you. Here are a few ways to check.
Search for their username:
Try searching their username. If no results appear, that means they have blocked you. But there could be another reason as well. It can also be that they have deleted their account.
Check chat history
Find your chat history with them. If it doesn’t appear in your chat history, it is most likely that you’ve been blocked.
Try sending them a message
Try sending a snap or a message to them. If it stays grey or pending, then this is another signal that they have blocked you.
Try finding them on another Snapchat account
Ask your friend or family to see if their username shows up to them on their Snapchat account. If it does, that means you’ve been blocked.
It is always good to check with multiple methods to get confirmation whether you’ve been blocked or not.