As someone who has had test anxiety, failed ADN school, passed PN and BSN programs, and the NCLEX twice the first time, it IS possible to have a plan to conquer your test anxiety.
Nursing school WILL NOT, I repeat WILL NOT hold it against you; they are very much aware of such challenges and they are common. In my PN program, they identified my test anxiety and with their suggestions at the BEGINNING of the program, I was successful-my ADN program did not identify it-I was doing EVERYTHING that they wanted to suggest to me already; the BSN program was very upfront and open for student who had past and current test anxiety. I added to strategies when I went for my NCLEX; and I knew how to tweak for my BSN program and for NCLEX-RN.
They will be very helpful in strategies for your success, however, It will be up to YOU to ensure that you get treatment for your anxiety; that starts with going your college and using their resources, as well as seeking out a professional to help with your anxiety.
Best wishes in your success.