As per information provided by you, your mother 89 years of age is having nausea
after more than 10 hours following PET scan.
I do not think this is due to any adverse reaction to the PET scan as such.
Still going by her age and that she has vomited 3-4 times, I suggest you take her to your hospital and get her examined by doctors.
We dont know but she may be going in for dehydration
, which at this age may lead to serious complications.