Re: We're not getting any sleep!
Yes, side lying works, and you'll get good at rolling over - either with baby on top of you, or scooting her under you as you switch. I also really like ltpyng on my back, with baby at 90 degrees across my chest nursing that way. Not sure when you can start that - I didn't discover it til recently with my 10 mo and so I don't know how much head control it takes. When I was getting REALLY tired of all the night feeding - maybe 4 or 5 months? - I did find that pulling my shirt down to cover my boobs would allow me to get an extra hour here and there.
But- it did also get dramatically easier for me, right about where you're at, as LO got head control and could latch himself so much better. So hang in there, because I bet the same will happen for you.
Nursing, pumping, cloth-diapering, babywearing, working professor mama with the awesomest SAHD ever.