My daughter and I both have this same problem. Sometimes what works for me is to excuse myself, or not depending, where I am and just go out of the store.
My daughter ( 45 yrs old ) has fainted and had a seizure at the clinic. It was decided the cause was a vaso-vagal reaction. So the minute she starts to feel dizzy and gets pale and clammy we just lay her down flat on the closest thing - even if it is the sidewalk.
Fainting, which is the common term for vasovagal syncope is very common. Fainting is commonly accompanied by other symptoms including dizziness and nausea just prior to feeling faint. Although there are many causes of fainting which have to be ruled out, the most common cause is Vasovagal syncope.
As you can see, our old friends from Anxiety/Panic often the cause of feeling faint.
Take care and remember you can always step outside.