Economics recognizes two types of inflation: cost-push inflation and demand-pull inflation. Demand-pull inflation follows the process you described, namely prices rise because too much money is pursuing too few goods.
The other type of inflation, cost-push, happens when the cost of goods rises independent of demand. Abuse of monopoly power can cause cost-push inflation (hello, business software pricing) but so can increased costs of labor.
On balance, cost-push inflation is a more probable outcome of the pandemic. It's physically harder to Do Stuff because workers need to stay further apart and because many will get sick and be unable to work. This will drive up prices to an extent, but price rises will be constrained by slack demand caused by reduced employment.
The other type of inflation, cost-push, happens when the cost of goods rises independent of demand. Abuse of monopoly power can cause cost-push inflation (hello, business software pricing) but so can increased costs of labor.
On balance, cost-push inflation is a more probable outcome of the pandemic. It's physically harder to Do Stuff because workers need to stay further apart and because many will get sick and be unable to work. This will drive up prices to an extent, but price rises will be constrained by slack demand caused by reduced employment.