In Gmail, there are a few ways to know whether or not you have responded to an email. Your options will depend on whether or not you are using Conversation View – You can learn more about this feature on Google’s support site.
Should you use Conversation View? It’s up to you! Feel free to test the feature out, and decide whether it’s a good fit for your workflow.
With Conversation View On
Navigate to mail.gmail.com and take a look at your inbox. If you have already replied to a message, a number should appear in the sender field to the right of the original sender’s name.
In the example below, John sent me an email, which I have replied to. The number to the right of John’s name corresponds to the total number of emails in the thread.
With Conversation View Off
From the inbox, hold your mouse over a sender's name (but don't click).
In the address card that appears, select Open Detailed View.
The resulting screen will show your open threads with that user, as well as recent events and shared documents. This should include your replies to the user, as well. Click on a given message or thread, to view the full thread.
Alternatively, you can run a search of your mailbox using the following structure: "from:me to:INSERTEMAILHERE".