The needs of the Navy change.
Generally Engineering and Math are preferred over Liberal Arts, Psych, Soc, Theo, or Poli-Sci majors.
I recommend that you locate and talk with an officer recruiter. There are less officer recruiters than there are enlisted recruiters. You will need to locate your regional recruiting headquarters, that should be the location where the officer recruiter has an office. Start by getting all of the phone numbers for that office. People individually will only be serving there for limited tours of duty, but usually the office phone numbers do not change.
Have a conversation and take notes.
Then save the phone numbers and notes; and call back in a year. A simple 10-minute conversation with the personnel in that office, should keep you up to date on which college majors are preferred each year.
I have known a number of enlisted men who put in 'packages' for officer selection. Your degree is one factor, but so is your motivation.
1. Why, exactly, you feel that you should be a Naval officer?
2. How do you think that your background and degree would benefit the Navy?
These need to be answered in essay form.
Also each region has a Naval Reserve Command. You may need to go there once a year. Make contact with any officer, introduce yourself and ask for an interview. Tell them about yourself and your desire to one day be an officer. Ask them for their advice, and finally ask them for a written recommendation. If you end up submitting a 'package' you will need three written recommendations from Naval officers.
As for your eyes, so long as it is corrected with glasses your fine.
Good luck