Welcome, Mamyefruge1!
To better help you we need the following:
• Whatever you know about where the pearls came from, their history.
• Photos in good focus of your pearls, taken against a white background (like a paper towel) in diffuse daylight (not direct sunlight), without flash
• Some of the photos should be closeups so we can see the surface of the pearl, any flaws, the drill holes etc.
• A closeup of the clasp front and back can be helpful. Tell us any markings that are on the clasp.
Clues you can use yourself:
• When you rub 2 pearls near the clasp together gently, is it rough or smooth? If rough, they are more likely to be real
• If you get a chance to look at them through a loupe (a 10x magnifier-- all jewelers would have one, and should let you look at the pearls with it) is the surface rough or smooth? (This is the opposite of the rubbing test: if rough, imitation; if smooth, real nacre.)
• If there are swirls of "nacre" near the drill holes, that is a buildup of fake nacre (fish scales + lacquer coating used to imitate nacre, also called "essence d'orient")
• Is there is a chipping away of the coating/nacre near the drill hole, revealing a bead underneath? Possibly a bead-nucleated cultured pearl.
• Is there a flaking away of the coating? May be fake, or low quality akoyas.