Care for New Mom

I have a three month, sixteen pound baby boy. He only falls asleep when being held, with me standing and bouncing him - often it takes several attempts for me to successfully put him down where he will stay asleep. As you can imagine, my back is killing me 100% of the time. Any other moms have been/are in the same boat? I’m finding it really hard both physically and mentally because I used to take such good care of myself - I simply don’t have the time now :(