An ascending aneurysm at 4.3cm should give you time to figure out your options. Most surgeons will not operate until an ascending aortic aneurysm reaches 4.5cm, at the soonest. If a thoracic aortic aneurysm is going to grow, it usually doesn't grow faster than about 0.1cm per year. So that would give you two years before it reached 4.5cm, if it even grows that fast. And a lot of surgeons do not operate until it gets to 5.0 or even 5.5. So you have time. Get as much expert counsel and do as much reading on your own as you can, and then when it is time for surgery (if ever), you will have a good foundation of knowledge for making all the decisions that you will need to make.
Yes, you will need to be checked for heart valve disease, which can accompany an ascending aortic aneurysm. Either the surgeon or your PCP should be able to refer you to a cardiologist. Your surgeon should have extensive experience in aortic surgery and not just in "general" vascular surgery. It is also highly preferable if your cardiologist has a special interest in valve disease. Treatment outcomes are good for people who get expert care. I am a survivor of your kind of aneurysm myself and have a mechanical aortic valve. Good luck.