Sorry to hear about your problems, Elle!
Finding a good pro waxer is as hard as finding a good laser or electrolysis practitioner.
The most common cause of skin tears is use of topical exfoliants, especially prescription topicals like Retin-A (trentinoin). Other prescription drugs such as hormones can also thin the skin, so you should speak to a doctor before waxing if you are taking any prescription drugs. Some consumers may get tearing if they use exfoliants like Tend Skin or other ingrown hair treatments, or a lot of lotions with alpha-hydroxy acid in the area treated.
It’s also possible to tear the skin if the wax is applied too hot or if the skin is not prepared correctly. A dusting of talcum or baby powder before applying the wax can often help reduce the chances of these types of industry.
A good waxer should not tear the skin. It’s possible they were pulling the strips away improperly.
In any case, this can be a potentially serious problem and can cause scarring. You might look into another place.