Don't fool around with this. While Mayo has fantastic cardio staff, you cannot travel without addressing the issue first. If Mayo does not have a PA who can see you first, find an outside cardiologist.

You need to be on an anticoagulant -- that may only be an aspirin or one of the prescription ( the novel oral anticoagulants [NOACs] that inhibit throbbing, or old fashion Heparin, which requires careful monitoring and diet restrictions.

Also, flying will increase your risk of a thrombosis. Wear appropriate support socks.

Because of the above mentions drugs have risks depending on your current physiological condition, you need to coordinate with a physician. Perhaps your family physician can be your first call.