Williams said she had no idea of how ill she really was until doctors discovered the life-threatening clots during a CAT scan.
"Mine went from my leg to my lung. It travelled fast," she said.
"I still have several clots in my lung and they are still there. They have to eventually dissolve. I'm taking it a day at a time."
Williams has not played competitively since winning last year's Wimbledon championship in July. Shortly after the victory she cut her foot on broken glass at a restaurant in Germany.
The American has had two operations on her foot since then but recently developed a hematoma, which she believes was caused by the combination of her prolonged break and frequent flights.
"Because I'm on blood thinners and on the injections...I must have hit something," she said.
"Usually, your blood naturally clots around it (but) since I was on blood thinners it wasn't able to clot.
"So what started as a golf ball ended up being a grapefruit in my stomach."
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