> But inflation should have been limited to the amount of money injected in the economy.
I'm curious to hear more about why that would be the case. Money swaps hands constantly and we have explicit ways that a single dollar can become many multiples of itself (aka you get a dollar, you put it in a bank, the bank lends me 90 cents, I put it in a different bank, they lend you 81 cents, one of us gets another loan secured by our assets, etc, etc, etc, now how many dollars are there?).
It's a bit ramshackle, but we have a pretty consistent way we measure money supply in the US: https://en.wikipedia.org/wiki/Money_supply
What you are describing is referred to as the "velocity of money" - how many times the same dollar changes hands, which there is a rough approximation baked into the monetary supply analysis - https://en.wikipedia.org/wiki/Velocity_of_money