Actually, if you get above a 93 on the ASVAB you in most cases aren't required to take the NFQT as you are considered pre-qualified.
taking the NFQT is not based on your asvab score, its based off how you performed on certain multiples. (i.e. if you sucked on the math section, but destroyed the rest of the test, you will most likely have to take the NFQT).
That said, enjoy the last multiple choice test you will ever take, sans rating exams... (pending you pick up nuke)
My 2 cents, you have 3 years of college. Unless you are in dire straights, and completely broke, Id go ahead and finish your degree. It really doesnt matter what your major is, I know officers with History degrees O.o Albeit, you probably have a higher chance of being accepted with an engineering degree of course.
couple tidbits for you, so you dont get screwed over,
1) take the asvab again and get over a 95. this allows you to receive an "Asvab score bonus". Only a few hundred, but its still nice

2) you have 3 years of school meaning you get a "college kicker". thats an ENORMOUS jump in your bonus pay (8k when I joined, probably more for you now).
3) your enlistment bonus is pending the time you join (i.e. Feb has higher bonus then oct). not sure why, but thats how it works.
4) dont let your recruiter run you around. As of this point, you are in complete control.
5) good luck
EDIT: found some info for you
Here are the test score requirements for Nuke;
VE+AR+MK+MC+NAPT=290
Or
AR+MK+EI+GS+NAPT=290
Or
VE+AR+MK+MC>252
Or
AR+MK+EI+GS>252
NAVY ADVANCED PLACEMENT TEST (NAPT)
a. Description. The NAPT is a two-hour, service-unique, supplementary test for potential Nuclear Field (NF) Program applicants who do not qualify based solely on ASVAB line scores. NAPT scores are valid for two years. The Navy administers the NAPT to prospective applicants when they meet any of the following minimum pre-screening criteria:
(1) Score 65 or higher on the AFQT.
(2) Rank in the top one-third of their high school class.
(3) Maintain a “C” average or better in one year of algebra.