John Parra/WireImage
Jennifer Garcia
March 10, 2011 10:55 AM

A fearless competitor on the court, Serena Williams admits she was terrified by the medical emergency that sent her to the hospital last week.

“I could have died,” Williams, 29, tells PEOPLE in this week’s issue of the pulmonary embolism and subsequent hematoma that she suffered.

Not grasping the reality of the situation at first, Williams says she felt shock and disbelief. “This can’t be happening to me,” she recalls thinking.

RELATED: Serena Williams Speaks Out on ‘Scary’ Blood Clot

But it was happening – and it was serious. Pulmonary embolism is a blood clot in the lungs, and a hematoma occurs when blood leaks out of the vessels and gathers in one spot.

The hematoma, in particular, was unnerving for Williams, who didn’t know what was happening. “I started panicking,” she says. “I thought I had a tumor.”

The hemotoma was successfully removed by surgery, and the 13-time Grand Slam singles champion is currently taking blood thinner medication and things one day at a time. But she hopes to be back on the court again soon. “I like having a challenge,” she says. “And this will be my biggest challenge yet.”

For much more on this story, pick up this week’s issue of PEOPLE, on newsstands Friday

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