I had an idea to create a real-time Instagram hashtag counter which would show how much a defined hashtag has pictures.
I got successful with the Instagram API part where I fetch the information, but I stuck at this point where I have to make the number of pictures count all the time, not only when I'm opened the web page.
Is it possible to get all the count of pictures with hashtags or I have to make some job to fetch the count all the time?
Use the real time api. Create a tag subscription for the tag you want to watch, and it will call a URL you specify everytime that tag was posted somewhere in instagram. Using code in that URL you can increment your counter.
For your purposes, you may not actually even need to call the api after creating the subscription, and can just increment by the # of items you get in each subscription post.