Juliet Hall, who was pregnant, was in labour and on her way to hospital when she was rescued by emergency crew from the flooded A30 nearby.
She was taken to the Royal Devon and Exeter Hospital by ambulance and gave birth there to a son.
The Environment Agency said two vehicles fell into Ottery St Mary's Firs Brook, one getting wedged on top of the other, which may have exacerbated the flooding.
Car owner Martin Ashfield said: "I woke up this morning and the car was missing. It had obviously floated away.
"The Environment Agency called me and told me where it was."
Elizabeth Devay, who was staying with five members of her family in a caravan near Ottery St Mary, said: "We heard a lot of rain and huge hailstones hitting the caravan roof.
"When we opened the door there were floods outside the caravan knee deep with the hail floating on top. By the time we got out of the door it was up to our waist."
Martin Ashfield's car was swept away by the flood
John and Joan Burrows, who farm nearby, lost about 30 sheep. Joan said: "Others are sheltering on the old railway line and we're hoping they don't try and jump in the water."
The town had been preparing for a carnival this weekend, ahead of its annual Tar Barrel Rolling festival on 5 November.
Devon and Cornwall Police said that roads in the area were "treacherous" and a number of routes were closed because of flooding or ice. Rail services were also disrupted.
In Boscastle in Cornwall, six premises were flooded overnight because of a blocked storm drain.
The Environment Agency has flood warnings in place on the Rivers Otter, Axe, Clyst, Coly, Culm, Isle and Yarty in Devon.
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