Household incomes rose in February as the unemployment rate dropped and employers scrambled to hire new workers. Personal income increased by 0.5% in February over the prior month, a pickup after it was nearly flat in January, but inflation rose more quickly. Income after taxes, adjusted for inflation, fell for the seventh straight month in February to the lowest level since March 2020, the Commerce Department said.

The data add up to a picture of the economy growing as shoppers benefit from a strong labor market and rising wages, but see those gains eroded by rising inflation, economists said.

Inflation “will be an even bigger drag in March with surging energy prices in the wake of the Russian invasion of Ukraine,” said

Gus Faucher,

chief economist at the

PNC Financial Services Group.

Consumer prices rose 0.6% on the month and 6.4% on the year, a new 40-year peak as measured by the department’s personal-consumption expenditures price index, the Federal Reserve’s preferred gauge. Annual core PCE inflation, which strips out volatile food and energy prices, rose to 5.4% in February.

In February, the wave of Covid-19 infections from the Omicron variant faded, leading consumers to spend more on services like dining in restaurants and traveling. Services spending rose by 0.9% in February, the most since last July, while goods spending declined by 1%, largely due to lower spending on vehicles as prices continued to rise and supply chain issues hurt availability.

The shift toward services spending shows consumers rebalancing after Omicron hurt demand for restaurant meals and entertainment and forced some Americans to cancel travel plans.

Travel, both for leisure and business, has rebounded faster than expected from Omicron, airline executives said. Major U.S. airlines said earlier in March that their revenues in the first quarter of 2022 will likely be at the high end of what they had expected at the start of the year, or better.

Kim Cook, the owner of Love to Travel, a tropical destinations-focused travel agency in Overland Park, Kan., said that her customers aren’t letting high airline ticket and hotel prices deter them from booking trips, especially with large groups of friends and family.

“They say, ‘I know it’s going to be pricey, but we haven’t been anywhere in two years, we really want to do this,’” Ms. Cook said. After building up savings during the pandemic, “they’ve got the money to burn.”

New applications for U.S. unemployment benefits rose slightly last week, but remained near historic lows, indicating a strong labor market in which employers are holding on to their workers amid high demand.

Consumers are sending mixed signals about how they feel about the direction of the economy. The Conference Board’s consumer-confidence index for March showed that consumers are optimistic about the Covid situation and the labor market but are concerned about the future impacts of Russia’s invasion of Ukraine on inflation. The invasion pushed up energy and commodity prices, adding to snarled supply chains and goods shortages that were already exacerbating price pressures.

“The outlook going forward is definitely not as rosy as it was,” said Alex Lin, an economist for

Bank of America.

“We’re expecting growth to slow down and consumer spending to slow with it.”

While companies for the most part say they can pass along price increases, they warn there are limits to what consumers will be willing to tolerate before high prices begin to cut into demand.

Inflation and shortages have already pushed consumers to switch from more expensive brands to cheaper options, survey data show. About 70% of U.S. shoppers said they had purchased a new or different brand than they had prepandemic, according to a survey conducted from May 2020 to August 2021 by private-label consulting company Daymon Worldwide Inc.

“Prices will force the consumer to shift,” said

Lindsey Piegza,

chief economist at

Stifel Financial Corp.

“When you’re talking about disrupting two economies that play major roles in energy and agriculture, that will affect consumer staple prices.”

Meghna Marathe, a 29-year-old consultant in Jersey City, N.J., is expecting her first child in August with her husband. She said impending parenthood has made her much more cost-conscious than she usually is, a change that has only been exacerbated by inflated prices.

“I’ve always kind of been able to, for the most part, not hesitate to purchase something,” she said. Now, when she is out shopping for the baby, she is more cost-conscious and focused on what the baby needs, rather than what might be “just fun to have.”

“A lot of expecting moms go into stores and see all the cute stuff they can buy for the nursery—I’ve been window-shopping, but I haven’t bought any of that,” she said.

Write to Gabriel T. Rubin at gabriel.rubin@wsj.com