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As for what over9k said I largely agree, and actually its a Neo-keynesian fallacy that interest rates are the main factor in controlling inflation with higher interest rates equaling lower inflation and lower interest rates bringing higher inflation. The empirical evidence does not support this idea nor does simple logic. As you pointed out raising interest rates raises the cost of capital for businesses which makes investment less attractive compared to the risk free rate and at the same time increases the cost of borrowing due to higher interest costs which means that fewer new investments are viable. Also business eventually tend to pass cost increases on to consumers. Just like if electricity prices rise or cost of goods sold rise businesses will pass that additional cost onto consumers in the same way if a company is now paying more interest on its loan to the bank due to higher interest rates it will also try to pass that cost onto consumers hence its inflationary.

Yes obviously rising interest rates lessens appetite for borrowing and destroys demand and so its a tug of war between the forces I explained above and this and its not always clear which was the tug of war will end despite central banks believing that higher interest are always dis-inflationary.

 If you want to stop inflation you need to stop the money printing and move to a hard money standard (gold, bitcoin, etc). Also economic and tax reforms need to be implemented to encourage higher supply of goods and services.