Instagram (and many other websites) sit on a lot of data. One way for users to access this data is through there website (web interface). Which is great for humans, not so much for computers.
This leaves us with two options: use web scraping, where we scrape the website for the data we want to have. But this means extract the data from the html.
the alternative (second option) is to use the API Instagram offers:
Instagram Graph API - Instagram Platform - Documentation - Facebook for Developers
The developers working at Instagram have also developed this API (application programming interface) besides the web interface. This allow us to write code to automate tasks
I have never worked with this specific API, so not sure if it offers the features you need, but it something you will need to look into
your own PC? Simple install MySQL (or whatever database engine your prefer and suits your usage case). Choice a language to use the API or web-scraping.
Doubt it, this would mean Instagram would need to emit some kind of event to which you can listen. You can of course run a scheduler to trigger your script every 5 minutes to fetch the latest data?