Hi - It's good that the lump you feel is moveable - most breast cancer lumps are fixed and immobile. Also, pain in your armpit and down your arm isn't a typical breast cancer symptom. And cancer running in your family (unless it's your mom or a sister with breast cancer; or your grandmother plus at least one other close relative with breast cancer) doesn't qualify as a family history that'll increase your breast cancer risk. So thankfully, from the symptoms you describe, the odds are on your side that this isn't breast cancer.
Still, any breast lump has to be diagnosed; it sounds like the mammogram was inconclusive, so your doctor is taking the next step: another, more focused mammogram, and an ultrasound. Oftentimes moveable lumps in the breast are fluid-filled cysts; uncomfortable, but basically harmless. There's a good chance the ultrasound will show whether or not this is a cyst.
If the ultrasound is also inconclusive, then you may need a biopsy. Scary word - but don't panic! About 85% of breast biopsies are negative; no cancer. So the odds are still with you. Finally, 95% of all new breast cancer diagnoses are in women age 40 or older; again, good news for you.
Bototm line: pursue the testing till you find out what's causing the lump and armpit/arm pain; it's the responsible thing to do. But please try not to stress too much; chances are good you don't have cancer. Take care- PJH