There is a section in the NSI packet which states the following....
"Due to the level of strenuous activity Midshipman Candidates will experience at NSI, you are required to provide documentation of your Sickle Cell Trait (SCT) status. SCT positive individuals must provide Hemoglobin (Hb) electrophoresis results (if previously completed). Most states required newborn SCT testing beginning in 1990."
Assuming a doctor has assessed you to not be positive for sickle cell trait, you should be fine.
But, there is an email address to specifically answer those types of questions. I highly recommend you send your question to grlk_nrotc_cgo@navy.mil
They are the best ones to field a question like that. Your NROTC unit can also help, but the email address above is your best resource.