In my opinion going to CIA after this would be overkill you best bet would be to get out into the industry. You might pick up a few bits and pieces at CIA but you will have pretty much covered everything at your first school. Remember this is a trade not like getting a degree in psychology where you need a masters.
What are your goals why do you feel attending two culinary schools will help you meet those goals. Recently I taught a class in Delaware to some students in a trade school and was truly suprised by how many of these students felt the need to spend more on culinary education. They had or will have spent 3+ years cooking every day and learning from excellent instructors. After that going to a big name school is either just for fun or overkill.
It takes time to build up your resume and also you will do much better if you find a pastry chef who runs his own shop and is profitable. Work for him for 3 years and learn how he makes his money. School teaches you how to cook but very little about running a profitable shop.
My advice get in the field as soon as you finish your junior college program.