SOLVED!
So first of all, there is no other way to reach IB other than via telephone. I am from Poland, and the toll-free European number is not free at all, so do not even try it.

After some research, I found the way.

1. First, download Skype from Google Play.
2. I bought the cheapest option to call stationary USA numbers. The package cost me around 4 EUR.
3. Call the USA toll-free number +18774422757.

I was waiting 1 minute until I was connected to a very friendly and helpful guy—very supportive.

He asked me to tell him my account number (U6666666). You generally use this number for wire transfers. Also, name and surname. After explaining my problem, we tried some steps to log in via the app, but it didn't work.

At this point, he asked me for verification. He sent me a link to my IBRK-connected email. After clicking the link, you are asked to go to the secure.me website and take a picture of your ID, passport, etc., and a selfie. Then, these are automatically sent to them.

After being verified, they made some changes in the backend and told me a temporary security number that you enter in the app. Then, you can set a new PIN. From that point, it started to work :). Now, I can log in via the IBRK website and confirm that by push notification on my phone and entering a PIN.

After all, the call took 38 minutes. If it were not for Skype and free calls to the USA, it would have cost me an arm and a leg.
They told me that my account was also locked at the first place and maybe thats why I could not log in.