We went through a rocking-to-sleep-only phase with my dd. I think she was 20 pounds by 5 months old, so I understand how taxing it can be on your arms/back. 15-20 minutes of rocking doesn't sound like that much compared to how long it would take my dd sometimes. Are you using just a rocking chair? Can you mix it up to give some relief to your different muscles? Some ideas to try...
1. Various pillows to prop arms on to make holding baby in the rocking chair easier and to mix up arm positions.
2. Using a baby carrier while dancing... the rocking step of a waltz works like rocking. Dd LOVED to fall asleep waltzing either in arms or in a carrier.
3. Different rocking chairs with different armrests to mix it up... we used a vintage folding rocker and a porch swing some in addition to the glider. Also a desk chair that swivels might be enough, just going side-to-side a little.
4. A baby swing... we didn't often use "contraptions", but the swing was a last resort sometimes when my arms gave out. Usually dd preferred to be in my arms but the swing worked when she was overtired.
I'll try to remember other things we did, but I think I've blocked a lot of it out! As for the frequent night waking, my dd did that for a long time... she would wake up to breastfeed, then wake up because she had to pee, then again when the diaper got uncomfortable, would go back to sleep but then wake again during light sleep because of the wet diaper. If you're not already, you could try changing wet diapers during the night instead of waiting till morning. You could try offering the potty during the night when he wakes if you're up for trying elimination communication. Both of those things helped us get through various phases of frequent night waking... there were other phases for frequent night waking too, like growth spurts and teething (which led to more night feedings/wet diapers) and developmental phases like learning to crawl and walk. But these phases will pass.
It's really hard for me to fall asleep after being awakened from a dead sleep too... I thought I was going to go crazy getting up 5 times a night to pee when I was pregnant this last time. Usually I can fall asleep pretty well the first time or two, then I can use breathing and relaxation to help fall asleep another time or two, but after the 3rd or 4th time and it's after 3 or 4 in the morning, I might as well just get up and do something because there's no way I can relax after that.