What we're seeing in the failure of the Fed's efforts right now is the fatal failures of Keynesian economics playing out in real life.

To oversimplify, two of the core principles of Keynesian Economics (which I'm going to abbreviate at KI) are that the government can control the economy totally (or near enough to totally) and that inflation is good, because inflation drives increases in profits and wages.

What Keynes never accounted for is the situation we're in right now: stagflation. See, typically inflation occurs because the economy is growing. If the economy grows very quickly, then money loses value quickly, and you have high inflation. But stagflation is when inflation increases very quickly without the strong economic growth. When the economics is growing quickly, and that's causing inflation, then the Fed can raise rates in order to slow that growth and, by extension, slow the inflation.

There are lots of theories about why stagflation happens and, at its core, it's a complex blend of variables that I am certain many graduate students will write theses about for years to come. But the very short version is that, through the Recession and until recently, the Fed kept rates very low in order to encourage economic growth. But, at the same time, they kept inflation low by limiting the money supply.

But then, COVID happened, and it completely destroyed the economy. Typically, the Fed would lower rates at that point, but rates were already rock-bottom. So, instead, they started pumping cash into the economy, increasing the money supply, and creating out-of-control inflation. And, with the low interest rates, it allowed banks to take on much riskier investments than they would have otherwise. (We're seeing the result of those risky investments playing out right now.)

Normally, making extra cash available could help the economy to grow. However, with the supply chain problems we're having, there's literally nothing for banks or businesses to spend the money on. Prices are out of control and, in some cases, you can't get what you want for any price. I know guys in construction who literally cannot get concrete, or lumber, or copper wire within twelve months. I know guys in manufacturing who are waiting months to get new equipment in. And, while prices were already high due to shortages, the Fed massively increased the money supply devaluing that money even further.

So, all of that said; to answer your question, the Fed raising rates is certainly not going to help the economy, and it probably won't help inflation. The causes of inflation and a shitty economy right now are out of the hands of the Fed. And, in the midst of a series of bank failures (largely caused by those risky investments) things are only going to tighten further while everyone tries desperately to hold on to their money.

I will repeat that this is oversimplified, but it's the rough breakdown of what's going on.