If “in your throat”, “runs in family” and “silent” are the three links, then the most likely is medullary thyroid cancer. Of the three major types of thyroid cancer, it is the primary form of thyroid cancer that is inherited. You certainly should try to find out from her what she has, and what your other family history is so that you can (perhaps) undergo genetic testing to best understand your risk. Management of this cancer involves complete and total removal of the thyroid gland (and neck dissection). Blood testing for a protein called calcitonin is used to measure recurrence. Has she had a complicated neck surgery? Is she taking thyroid hormone replacement? That would help figure this out.
Another alternative is lymphoma or leukemia, which can often be “silent” and would go with your mom’s description of measuring her counts. Lymphoma can be found in the lymph nodes (maybe in her neck), and CLL, a relatively mild form of leukemia can be measured in the blood.