What happened to Winnie and the pebbles?

I'm assuming you're referring to Winnie's first meeting with Jesse Tuck, which takes place in chapter 5 of Tuck Everlasting. While Winnie's happily wandering through the woods, she comes across a clearing. From a distance, she watches a handsome young man lift up a pile of pebbles to expose a bubbling stream of water, from which he then takes a drink. Winnie thinks she's well-hidden, but Jesse knows that someone's watching him and calls out to whoever's there to come out of hiding.
Winnie duly does so, and soon she and Jesse are engaging amicably in small-talk. Winnie's understandably curious about the stream of water beneath the pebbles and asks Jesse if she can drink from it. Unbeknownst to her, the fresh spring water brings immortality to those who drink from it, and Jesse, who is himself immortal, tells her it's a bad idea. But Winnie, being the headstrong, willful young lady that she is, ignores Jesse's sage advice and gets down on her hands and knees to sample what she doesn't yet know is an elixir of eternal youth. Thankfully, Jesse's mother and brother arrive just in the nick of time to prevent Winnie from joining the ranks of the immortals.