What sort of things can cause tingling sensations in your teeth and gums?

Gingivitis: The bacteria and other particles, constantly form a sticky, colorless toxic “plaque” on teeth causing the gums to become inflamed, painful and numb ( tingling sensations) easily bleed. This is a serious problem, called gum disease (gingivitis) which should be checked and treated by a dentist.

Tingling: lots of possibilities, including but not limited to, gingivitis (infection), abscessed (infected) teeth, allergic reaction to foods/medicine/OTC's/environmental allergens, blood dycrasias, neoplasms, systemic disorders. In other words, n you need to be examined to be diagnosed. Please see your Dentist.