Let me toss this in here; receiving a commission as a Naval officer is NOT signing up to be an engineer. You're going to be a program manager on a divisional level, i.e. Machinery Division, Electrical Division, Reactor Controls Division, etc.
That comes AFTER you spend time at SWO (Surface Warfare Officer, if you end up that path) school in Groton, CT then 18 months on a non-nuclear ship like a destroyer or frigate as a division officer for some division. After that 1st DIVO tour you'll go to Charleston, SC, for 6 months of Nuclear Power School, followed by 6 months of prototype training either in Charleston, SC or Ballston Spa, NY.
After all that, you show up on a carrier, either in Norfolk, VA or San Diego, CA or Everett, WA or maybe in Yokuska, Japan. By this time you'll have roughly 3 1/2 years left on your commission. During that time you'll be expected to qualify as Propulsion Plant Watch Officer on a plant that you've never seen before, integrate yourself into your new division, get yourself up to speed on who your sailors and Chiefs are, figure out who is who as far as the "hot" runners, the middle-of-the-roaders and the derelicts while juggling all of the nuke and non-nuke programs that you'll be responsible for. After about a year of being qualified, the Navy will ship you off to start studying for your engineer's exam. Based on past experience, that can take upwards of 6 months of your time. By this time you'll be down to around 18 months, maybe less, until you have to either extend your commission or resign it. The Navy will toss some decent sized bonus money in your face and you'll either take it and stay or decline it and resign your commission, becoming a civilian with zero years of experience as a Chemical Engineer.
The purpose of this paragraph isn't to rain on any of your plans; it's called a reality check. Naval officers are meant to be leaders. Nuke officers don't do anything that resembles being an engineer for the vast majority of their time on Active Duty. If that is the reason you want a commission, you're going to be disappointed and resent the Navy for not providing you something that honestly, isn't a realistic expectation. If you want a commission in order to serve your country, develop leadership skills and add some leadership experience to your resume, then by all means head down this path.
Lastly, MMM is on to something VERY important; if your resume reads anything like your posts, it's going to be an uphill battle for you. Your resume is a potential employer's first chance to look at you. Your poor written communication skills, which is a vitally important skill both as an engineer and as a Naval Officer, don't paint a picture that makes a manager think "This recent college grad is someone I want representing my department in our company.". Tough and brutal appraisal? Yes. Honest and up-front? Absolutely.
Gamecock and Spekkio are our resident members who most recently were officers on Active Duty. Ask them for more info.
Best of luck and don't rush into this decision. Otherwise, you could waste at 6 years of your life doing something that you may despise.