Yes, it is your quilt, and yes, you can do whatever you want. But if you are unhappy with the way your corners look when you use a continuous binding strip, you will probably be even more unhappy with the way they look when you do each side individually. You will be turning the binding under at each corner, and that adds bulk, which will make it very difficult to sew that corner and make it really square. Chances are it will stick out in an awkward manner. I would say - try it on one corner. Just sew one piece of binding a few inches down the quilt to the corner, and then sew another on the side that meets that corner and try out your technique. If it works for you then continue to do the rest, and let us know whether it works or not.