Hi and welcome. Whatever is going on, I think it is only coincidence that it happened around the time of your visit to the vet. You also seem to have 2 different issues on hand–1 are some medical concerns, and the other is potential behavior issues that have arisen from the arrival of a new puppy, a situation that is not uncommon. Even if dogs play together, it can still be quite stressful to a dog that has been a solo dog at home to suddenly have a permanent companion and can take quite a while for things to settle down. I would certainly try to do a lot of activities that are separate but equal with your 3-year-old eg, take him for walks on his own as well as with the puppy, and give him lots of direct attention. He actually needs more attention than the puppy will, just for reassurance as things settle down.
The howling at the door when you've taken the puppy out would not be uncommon–he's just frustrated at being left alone in the house while the puppy gets to go out. I would just ignore that kind of behavior, but I would also give him something pleasurable to do when the puppy goes out–for example, give him a Kong stuffed with something interesting but low calorie, such as mashed banana mixed in with a bit of dry food, or else, take the puppy out while he stays at home and has his morning meal in the Kong, etc. Kongs are one of the single best toys ever invented–they are very reassuring and comforting to dogs and also keep them quite busy. There are lots of threads on Kongs and how to stuff them that you can search for–some especially good ideas are low cal yogurt or banana as the base, adding in a few crunchy goodies like dry kibble, and then freezing the whole thing as that makes it last much longer for the dog. A small or medium-size Kong suits Cavaliers.
On the medical issues–it is just very hard to tell what is causing this. SM can come on very quickly, yes, and also people can easily miss some of the earlier signs, thinking it just to be normal scratching and so on. But I also would think there might be a other reasons for why he is doing this and it might be worth seeing a different vet to get a 2nd opinion, at a different practice. With that kind of behavior, I'd be wondering about flea dermatitis, Rabbit mites (did your vet do a skin scrape test for the presence of mites? Many vets can miss them and they often congregate around the base of the tail and cause frantic scratching and discomfort) or perhaps allergies of some sort.
If nothing else is working and there is a suspicion of SM, you could talk to your vet about using Dr. Clare Rusbridge's treatment protocol, which you can download from her website. She also has a document there that vets can read that gives lots of background on SM. If the medications for SM work, then you would know that that is likely what your dog has, and you can work on treating with medications without going the route of a costly MRI, at least initially as you decide what you wish to do. An MRI will give you a lot more information, confirm diagnosis, and would be necessary if you were to consider surgery. But given the expense of doing an MRI, and the frequency with which this condition appears in the breed, personally I think it makes more sense for many people to just try working with the recommended treatment protocol to see if that begins to help, as that is also pretty much a confirmation of diagnosis (However, many vets will not wish to undertake treatment without having a diagnosis or at least input from a neurologist and will want the owner to take the dog to a neurologist 1st). Another alternative is to see a neurologist for a clinical visit, but explain that you can't afford an MRI. Often, a neurologist can give a pretty good indication on a clinical exam, looking for various other signs of the condition, as to whether it is likely the dog has the condition or not.
All that said, only an MRI can give a definitive diagnosis. And if you do find that you are dealing with SM, I'd be sure to let the breeder know as they should MRI their own breeding stock, if they are not doing this already. There are many low-cost programs that would enable them to do this in the UK, and hence, no excuse for any responsible breeder to neglect this important step in working towards breed health.