Tires damaged by too little air – replace

Hello, when I was driving the car yesterday, I noticed after a few kilometers that the car was swimming. So stopped and looked. A tire was pretty flat. With a foot air pump I pumped the tire again and adjusted it again at home with the compressor. However, the tire (probably through the wheel cap / rim) has a damage on the outside (see photo). Can I drive the tire still further or do I have to replace it? The tyres are only 4 weeks old