ILL: Mariah Carey, 32, checked herself in a hospital Wednesday night, suffering from “extreme exhaustion,” says a spokeswoman in London. No details, including the name of the hospital, were provided. The rep, however, did say that the pop star had just finished shooting two movies, “Glitter” and “Wise Girls,” as well as writing, recording and producing the soundtrack to “Glitter.” No word on whether or not Carey will have to bow out of her singing engagement at next Wednesday’s “MTV20: Live and Almost Legal” birthday bash . . . SUED: Courtney Love, 37, is being sued by landlord Peter Ashby for failing to pay more than $40,000 in rent for a home in British Columbia, where she was shooting a movie. In her legal papers, Love, who is seeking a dismissal of the case, says the house wasn’t suitable so the lease was never executed. No trial date has been set . . . SOLD: ‘N Sync’s latest CD, “Celebrity,” hit stores Tuesday, and industry watchers are estimating sales of nearly 2 million units by next Monday. That’s down from the record-breaking 2.4 million copies that the boy band’s “No Strings Attached” sold in its first week last year, but it’s still more than enough to make “Celebrity” the biggest debut of 2001 to date (eclipsing the 730,000 copies sold by the Dave Matthews Band’s “Everyday”) . . . ENGAGED: Model-actress Andie MacDowell, 43, accepted an engagement ring last week from Rhett Hartzog, 43, an Atlanta jewelry businessman, whom she has known since grade school, says her father. Marion McBride said his daughter plans to marry in November in Asheville, N.C., where MacDowell lives. It will be her second marriage.