It sounds like they're recommending you for genetic testing not genomic testing (which is what I had) if it's HBOC. I don't believe this will impact on their treatment decisions.
An endometrial ablation is where they "burn" away the endometrium of the uterus. I had it done due to low iron from heavy bleeding. There are other hormone medications that may be more suitable if you have a uterine cyst. Your medical oncologist can help to explain all the options and the different side effects.
Good to hear that you have antibiotics already. Definitely take the full course, it won't cause any harm if you don't have an infection but will be well worth it if you do.