Is Kaspersky doing enough?

No your computer is not safe. If you ran a scan, and cleaned everything, then run a scan the next day and your infected again you have a problem. Kaspersky is not fixing it. I would say you may have a trojan driver install and none of the anti-virus programs are going to be able to remove it. Or you may have a nasty rootkit on your computer. You should at the very least try a safe mode scan with Kaspersky. Get malwarebytes anti-malware download, install, update and run a scan. You should also get an anti-rootkit tool and run a scan with it.