Premiere pro slows down my internet

Is this the case with all browsers? (In other words have you tried different browsers?)

What is your computer? Full specs OS/CPU/RAM/GPU, and how many discs of what type does your computer have?

What kind of media, and what effects, are you using in Premiere?

With that information we could give actual advice rather than guesses. But my guess is simply that Premiere takes  a freaking TON of computer resources to operate. And perhaps, if your rig is to the minimalist side for hardware, with Premiere 'active' your computer doesn't have the resources to do much else period.

No, I don't have any media stored online. I mean I open Premiere Pro and then internet in my computer collapses, I can't download anything. I generally can't enter even websites.

never seen this behavior.    Do you have any media stored online such as dropbox, icloud, etc?  If so, that could be the problem and it's never a good idea to work this way.   Unless you've invested in a cloud based shared media solution, this is not a practical way to work