The teenager – who suffers from Prader-Willi syndrome – had been suffering with a high temperature and shaking following his jab on Friday.
Harvey, 18, received the Oxford/AstraZeneca jab as his rare genetic condition means he falls within a priority group for the clinically vulnerable.
So far, more than 12 million people have been inoculated with a first dose of the vaccine.
It was reported that Harvey was taken to hospital on Saturda, experiencing shaking and a high temperature.
Price, 42, shared the news that her eldest son was “safe and well” in an Instagram story, shot beside Harvey on the sofa.
She told her 2.4 million followers: “Harvey obviously is home and he’s safe and he’s on form today.