Raising Interest Rates: Throwing Gasoline on the Inflation Fire

​I am not an economist. Basic economics makes some sense to me. Supply and demand is pretty basic and makes sense. Inflation makes sense. Too much money chasing too few goods and prices go up. What does not make any sense to me is how our national bank fights inflation. The logic of the inflation fighters is if you increase the interest rate the cost of stuff will increase thereby discouraging purchases. But wait a minute, is not increasing prices part of the definition of inflation? Fine they say, raising the interest rate only reduces the demand for loans, which discourages expensive purchases by consumers and curbs expansion by businesses.
So, if I as a consumer have a lot of cash but am discouraged about buying expensive items maybe I’ll take that money and buy a bunch of smaller items. In other words, sending too much money after the same amount of goods in the marketplace. Demand is up, prices are up, inflation is up. Exacerbating this, businesses are discouraged from borrowing so they cannot expand capacity to meet the increased demand for consumer goods. So, it seems to me that raising interest rates fuels inflation. It is like throwing gasoline on a fire. I would love a response from a competent economist or anyone else for that matter.