Maybe his ears or teeth are bothering him? The abruptness of it all sounds like how my daughter acted when whe had pain.
However, I think it is more likely a normal developmental thing - some separation anxiety and some maturity in realizing he can use his voice very effectively to get what he wants. My daughter wanted to be held all the time from about 13-18 months... and the whining really kicked into high gear around then.
I'm afraid that I don't have much advice. Just don't blame yourself because of the back issue, this was probably coming anyway. It sounds like you are doing all the right things in terms of encouraging trust and security. I guess I would suggest continuing to rock him to sleep at night. But during the day, try not to pick him up in response to screaming. Get down to his level, look him in the eye, talk to him, hold his hand, distract him with a toy, etc. But don't pick him up each time. As he enters toddlerhood, you need to think about how you want him to learn to talk to you, and screaming nonstop is not the way!! You are trying to teach him more mature self coping skills.
I found this age a hard adjustment, because you have spent their whole lives catering to their every whim, feeding on demand, reacting to every little sound. Then all of a sudden you realize that your child has learned to manipulate you. It is not naughty, it is just part of this age. He is starting to really test his power over you, so you need to start reacting to him like he is a little person and not a little baby. I am not saying to ignore him - and you cannot spoil a kid this age - do comfort him - but make sure he knows that you simply can't hold him continuously. That's reality and he needs to play independently a little bit and he needs to self-sooth. You just need to help him get over this bump in the road.
As much as it drive you nuts, he may just do this for a while. Once you get the daytime calmed down a bit, then you can worry about nights. I would just hate to see nightime become a battleground that could impact his sleeping. The only thing Iwould say about nighttimeis to not let him play on you at bedtime. If he sits in you lap chattering, fine - shush him, do't talk back, etc. But not jumping around and climbing on you. If that is going on, I would plop him down or pull him away from you and say "night-night, quiet time." He can't begin to associate bedtime with play or it will just make matters worse. Maybe have someone else put him to bed for awhile or wear him out at the playground in the late afternoon.