Not sure what you mean by a "sticky" heart valve--unless you mean stenosis of a valve. They should have been able to pick up some details about the heart valve on a transthoracic echocardiogram--but a TEE (transesophageal echocardiogram) is even better. In addition, if they are consider cardioverting you, a TEE will help them look for any clots that may be a contraindication to cardioversion.
A TEE is just placing a ultrasound probe in the esophagus to look at the heart. The reason we do this is that the esophagus sits right behind the heart (actually touches the heart) -- so the pictures are closer, and in better detail. Complications with the procedure mainly are due to complications of getting the probe down the throat. The probe is about the width of a finger, so you can imagine sticking a finger in the back of your throat, and the gagging that is associated with it. So we numb the throat with some nasty tasting spray and viscous lidocaine. In America, we sedate the patient for the procedure, but I have heard other countries do not sedate. However, the procedure is VERY safe---with a complication rate much less than 1/1000.
Hope this helps.