I don't know why you would assume they would not do a mammogram. That would pretty much be standard of care for a diagnostic work up prior to any other testing or anything invasive.
October is breast cancer awareness month, so now is great time to get checked out. Unless you are very young, you do not have to have a doctor's order to have a mammogram. Most places run specials the month of October and they take insurance too.
At the mammogram, there is usually a Dr. or nurse practitioner who will do an exam by feeling the breast tissue. especially if there is anything of a concern. If you do not have a dr. they will refer you.
Some places will even take walk ins, there is a brief questionnaire about your health.
The fact that you have swollen ankles is likely not related to the breast lump, but certainly a red flag that you need a complete head to toe assessment by a medical professional!
Do not put this off! Early detection is key for ANYONE who might be dealing with a cancer diagnosis. At this stage of the game, you don't have enough information to be second guessing about breast removal or chemo or radiation, much less whether you have cancer.
Most all major hospitals or medical facilities have "breast centers", so call around and you can get a price quote as well as an appointment.