I took a school approved co-op Spring 2016 and Fall 2016 and took classes on campus Summer 2016. While I didn't take classes during the spring and fall, I was still considered a student with it listing my co-op as a 12 hour (full time) course. I filed as a part time student because I only took classes during the summer but now I believe this to be a mistake. Is this the case, and can I change this if I have already filed?
Yes, if the co-op was (as it appears from your question) a school-approved program for which academic credit was granted, then you were a "more than half-time" student for the entire year.
If you have already filed, you should file an amended tax return claiming all of the qualified tuition and fees paid for the year. I am certain your school will have charged you fees, and probably tuition) for those 12 hours granted for the co-op.
TurboTax will guide you through correctly entering your new data and printing Form 1040X. You may also have to amend your state income tax return if you have a state income tax. Please note that amended tax returns must be filed by mail.
For more information, please see TurboTax Guide - Amending Your Income Tax Return.