When you have a car accident is it mandatory or normal for the insurance company to pay for pain and suffering if damage was done?

Unfortunately, you left out critical details, such as how and where the accident occurred, who was At Fault, whether all involved parties are insured, and of what "pain and suffering" you are referring. Regardless, "pain and suffering" is a matter for the courts, not the insurance companies. As with any other case, at least in the USA, if the courts decide that "pain and suffering" is warranted, then the offender's insurance company would, most likely, appeal the ruling. If the appeal fails, then that insurance company is obligated to pay, assuming that the at-fault driver is so insured; otherwise, the offender's insurance company would not be involved at all, except for peripheral details, and the offender would take the brunt of the claim. If the offender wins the appeal, then the victim should appeal. As you can see, this can take a lot of time, money, and effort.