Depends on the city you live in. Rent here has been going up for a long time - even when inflation was near zero. So for locals, the rent increase alone is not an indicator of inflation.
When people refer to "inflation" without any additional modifiers, they're generally referring to the Consumer Price Index numbers released by the government. When the news reports that "inflation is at a 40 year high" or "inflation is at 6%", that is based on the CPI. The CPI does not include housing costs. The most visible single component of the CPI for most people is the cost of gasoline. That's the only thing that I've personally noticed costing more.
That was stated surprisingly confidently. It's entirely wrong though, the CPI does include housing costs. I don't know why you would single out gasoline as "most visible", but I guess that gives you flexibility to claim that your real meaning is whatever you want. Gasoline prices actually (currently) impact CPI about half as much as food prices and one tenth as much as shelter costs.