WASHINGTON — Liz Szalay said she was shocked when she saw her 14-year-old son’s phone bill. Because he didn’t have a $30 data plan as part of his Verizon Wireless contract, he’d run up charges of $2,000 over two months for downloading songs.

“I would never have allowed my son to accrue such charges, if I had known,” said Szalay, a secretary in Niles, Mich., who said she withdrew money from her 401(k) retirement plan to cover the expense. “What I did to prevent this from happening in the future was have his Internet access completely blocked by Verizon, but not before they made off with a boatload of money.”

The Federal Communications Commission may make it mandatory for carriers to warn customers before they get hit with high bills. Next week, the agency will consider requiring companies to alert customers when they approach limits on their contracts.

Carriers including Verizon have fought against such requirements, saying they already give customers ways to monitor their usage.

Verizon, the largest U.S. wireless carrier, is also under investigation by the FCC for charging 15 million customers incorrectly for data. The Basking Ridge, N.J.-based company said this week that it will refund the charges, incurred when software inside its phones received or sent signals or customers were mistakenly charged for Internet access. The cost to the company will be about $50 million, a person familiar with the matter said.

FCC spokeswoman Jen Howard declined to comment about further steps in the commission’s investigation. Marquett Smith, a spokesman for Verizon Wireless, declined to comment on the proposal.

The CTIA, the wireless industry association, has resisted the idea, saying it will cause “customer confusion and frustration” and that carriers already offer customers ways to control their usage. Subscribers can check their usage with online monitors or via text message.

“We have several measures in place that allow our customers to monitor their usage and protect against overages — this is a proactive approach on Verizon’s part,” Verizon’s Smith said in an e-mailed statement. AT&T, the second- largest wireless carrier, and Sprint Nextel, the No. 3, deferred to the CTIA’s statement on billing practices.

One in six U.S. mobile-phone customers has faced unexpected monthly fees, according to a survey released in May by the FCC.