It never hurts to get a second opinion. The doctor should have explained why NP was being added. But not knowing your full thyroid history it is very difficult to give an accurate opinion. I am a believer that you go with your symptoms first. People thrive at different ends of the lab scale. Look for an endo that is willing to listen and seem to be flexible. Pour through patient reviews, check their medical credentials and background. Good luck!
I'm not sure I completely understand your medication... Am I correct that you started on 100 mcg Levothyroxine, then switched to 60 mg NP, then 90 mg NP?
Your Free T3 is over range, indicating that you don't need so much of the NP. T3 is 3-4 times more potent than T4 is, so it's not unusual for some of us to need additional T4 with desiccated hormones.
The low FT4 would tend to make you feel hypo, while the high FT3 would make you feel hyper. Aside from that, some symptoms (especially fatigue), can apply to either/both hyper and hypo.
What were your labs like when you were on the 100 mcg Levo and 60 mcg NP? If you could post those with reference ranges, it would be easier to advise. That said, it looks as though you could use less T3 and more T4.
In addition, have you had Vitamin B-12, D and Ferritin tested? Is so, what are your levels?