Turn on notifications for your favorite accounts
That way, you won't miss anything from the person you don't want to miss anything from. How do you do this? First, go to the account in question. Then click on the bell, at the top right next to the name of the account. Once you have clicked on it, you will see the menu in the middle screenshot. From there, you can turn on notifications for specific message types.
You can also turn on notifications for specific message types via a post or Story from that person. For example: see the screenshot on the right. I clicked on the three white dots at the top right of the post. The menu will then appear at the bottom, where you can choose 'Turn on message notifications'. This will turn on notifications for messages from this account.
Turn off notifications from less interesting accounts
Would you rather not unfollow an account, but would you like to see fewer (or no) updates from this account in telegram data your overview? Instagram also offers a number of options for this.
It may feel a little scary, but you can click the 'Following' button of an account without consequences. You do not immediately unfollow this account, and the person will not receive a notification. Instagram will first show you a few other options via this button.