I have a blog and an application that gives the number of comments and posts on my blog by using my blog's API.
The issue I'm having is that I want to have my application receive new comments from my application in real-time.
My solution:
I can have my application calling the API every 30 seconds or so to check whether there is a response (i.e. whether there is a new comment).
I think the best solution is to use something called Long Polling to get updates. Its a technique in programming to handle requests with less resources such as CPU being used over time. For a detailed solution for your case search for

Long Polling in Flask application
How to get new (real time) comments from my blog?