I have a rocker with ottoman and yet I find myself with my boppy on the couch and in bed propped up with pillows nursing more. Try taking a 10 lb item and use it to figure out what will be comfortable for long durations.
I don't see any medical help in your problem. but when we talk about privacy, any one need a privacy.
I am not sure a chair is really needed. I ended up nursing just about anywhere in the house with my Boppy pillow. It is a must recommendation for moms planning to nurse!!
I used a nursing pillow on my couch the most but if you want to buy a nursing chair, look for one that glides/ rocks, has high and thick arm rests (for nursing), and is comfortable. They can be really expensive. I saw some that were affordable at Wayfair but I'm not sure of the comfort level.