Especially in elder persons, blood pressure measurements can be experienced as painful. This is even more the case when the person has a high systolic blood pressure.
Of course I do not count you in the elder person's category. :-) Also younger persons can experience it.
The cuff is inflated above a systolic blood pressure so the arteries in the upper arm are fully blocked.
A higher pressure of the cuff is needed when the person has higher systolic blood pressure.
In some cases, the pressure can lead to bruising of tissue in the upper arm.
In your case, if it is bruising, it seems severe and I would certainly have a doctor look at it.
I.m.o. the behaviour of the assistant that took your bp leaves much to be desired, to say the least.
You could make an appointment with your doctor and just mention arm pain as the reason for your visit. Try not to discuss or debate your arm situation with the staff. When you see the doctor in private, explain how your pain came about and seek her advice.