As @aglages says, contact the NROTC unit at the college you wish to attend. Generally, yes, you should do this very early in the summer. See the following information from Iowa State University NROTC.
http://www.navy.iastate.edu/prospective-students/nrotc-college-program/
Also, the Navy loves engineering majors and it would almost certainly help in getting into OCS or STA-21. No way would it hurt you.
Good Luck!