This is what I read from Tulane's handbook specifically about Mid-Mid relationships http://tulanenrotc.com/wp-content/uploads/2014/04/Handbook-3JUL13.pdf
Midshipmen Relationships. Relationships between midshipmen are not considered fraternization. However, relationships between midshipmen within a direct chain of command may give the appearance of impropriety and should be avoided. In cases where such relationships cannot be avoided, the midshipmen involved need to bring the relationship to the attention of the unit staff. One or both midshipmen may be reassigned to different billets within the unit without prejudice to the midshipmen's performance records. It is the responsibility of all senior midshipmen to train and mentor the junior midshipman. Any relationship between 4/C midshipmen and NROTC upperclassmen jeopardizes training goals and is considered prejudicial to good order and discipline.
Somehow you will need to find out what your Battalion's policy is. I would assume that your unit's handbook is silent, I know my DS handbook does not mention fraternization. It would be nice to get @NavyNOLA
input on if and how you should ask you chain of command.