there is no need to panic. High blood pressure in someone your mom's age is not uncommon. More and more people are having to make changes to their lifestyle in order to reduce the risk factors of cardiovascular disease. Daily use of antihypertensive medication for blood pressure regulation is often necessary. We are lucky antihypertensive medication is available.
It hasn't been established that your mom has high blood pressure. Home readings are often unreliable due to people not taking the readings correctly. Same goes for office blood pressure measurements - often, errors are made. Blood pressure is variable. In many people (with or without hypertension), it becomes markedly elevated at the doctors' office. This is called white-coat hypertension. Blood pressure can also spike considerably when we are stressed, ill, or in pain.
Diagnostic procedures include repeated blood pressure measurements, taken on several occasions (often in both arms), as well as laboratory investigation. There are some basic lab tests which will likely be ordered. Should secondary hypertension be suspected, additional tests will be done.
The chances are your mom has been told to monitor her blood pressure at home for a week or two, and to take her pills. A date has been set for a follow-up visit. It is probably during this or a subsequent visit that laboratory workup will be ordered, the effectiveness of her drug therapy evaluated, and proper cardiovascular risk assessment done. The very fact that she was sent home with medication does not indicate any perceived urgency. It could take up to several weeks for her medication to become fully effective.
Hypertension is a very managable condition. The goal of treatment is to maintain normal, or near normal blood pressure levels. Some of the people on this board have lived with hypertension for a very long time. With the help of medication, it can be managed well and quite easily.