I might have something called coarctation of the aorta; what is it; can you treat it w/o surgery?

Maybe. Coarctation of the aorta is a narrowing of the aorta usually present from birth. It is most often treated with open surgery but endovascular stent grafts are being attempted. Medical management alone cannot change this anatomical problem.
Some try. This is a plumbing problem. The aorta has a narrow section that restricts blood flow. Since it is present from birth, most develop some extra blood flow in other arteries to get by but it is still a problem. A common fix is to go in with open surgery and replace the narrow part. Some try to fix it using a catheter to stretch it open & hold it open with a stent, but that has risks (could pop)
See below. A coarcation of the aorta is a rather severe narrowing of the vessel that carries blood from the heart to the rest of the body. If this is severe, or is continuing to narrow as you age, the blood supply to the lower extremeties and you abdominal organs can be compromised. The problem could be treated with surgery, or maybe by the use of stents.