It sounds like your current diet might not be too far off from what you would be recommended with NB. A lot of veggies are a must plus protein and no refined foods so I wouldn't worry too much about being able to handle the diet.
Before I started with NB I was extremely fatigued. Some days I could only shower and get dressed and then I was useless for the rest of the day. I had nausea, diarrhea, weight loss, depression, anxiety. That was at my worst.
I have been tested many many times at the doctor's office for thyroid issues and the tests always came back negative. But I've always suffered with being cold and a lack of energy. My hair analysis showed that I was hypothyroid on a cellular level and confirmed that all these symptoms I've been having for years aren't in my head.
I still have fatigue and anxiety, those are the most prominent symptoms along with occasional insomnia. It's been about a year and I feel 30-40% better.