Hi Emma–and welcome to the board!
I think the problem here is that there isn't any structure to your puppy's house training And he needs much closer supervision as well as restriction of movement. Basically, a puppy should never be able to go run off and use the carpet, and if he can, he's being given far too much freedom that he doesn't know how to handle.
Either he needs to be on your lap, at arm's length so that you can get him outside if he begins to look like he needs to go, in a crate, or asleep!
In general–it almost never works to just put a puppy outside and expect him to go -- he doesn't know why he's suddenly been put outside, and of course he is going to call out in distress and ask to be let back into the warm house!
At regular intervals (very frequently when he is really young, and then tapering off as he gets older), you need to put him on a lead, walk him outside, and stay outside with him so that he can be immediately rewarded with praise and ideally, a small treat as soon as he goes and so that you can make sure that he goes. If he doesn't go, he comes back inside and then is confined in a puppy playpen or in a crate for a set amount of time until he is taken outside again.
I would just get rid of the puppy pads–they are a waste of time because once you house train to the puppy pads, you then have to house train a second time to get your dog to go outside! It is hard enough to train a puppy once much less to have to go through the exact same procedure twice. If there is really no choice than a pad can be a place to start, but still, it should be placed within a confined area so that he quickly learns to use the pads. He's only a baby and will not know that he is supposed to go use them unless he has been trained by you to use them as his toilet. I think it helps to think about house training in the same way you would think about toilet training a two or three-year-old. They just do not have the ability to be shown once or twice what they are supposed to do and then be expected to go off and use the potty. Potty training for toddlers is a long process and takes many weeks to months. A dog owner can expect the same from any and house trained dog, whether puppy or adult.
And to be honest, it is always a challenge to house train, takes months for most dogs (Most owners in my experience mistakenly believe their dog is house trained long before he is, and thus accidentally let the dog regress back to going inside without realizing this is happening and then end up with having to do a lot of remedial house training. So really focus and give the time while he is young to make sure he never has the chance to make a mistake inside, and you will get the house training over with much faster). house training always needs to be done with gentleness, and kindness. Punishment only teaches the dog to go off somewhere out of sight somewhere else in the house because they will generally associate the punishment with the fact that they are not supposed to do this while you were there and watching, not that the issue was that they went inside rather than outside.
In the library section of this site there are several links to advice on house training, but to make things easy I would recommend that you just go to Dr. Ian Dunbar's website and download, for free, his book “After You Get Your Puppy”. This is an excellent book to help guide you through every aspect of owning a puppy. A positive, rewards-based approach to training is really important, especially with this very gentle breed, and this book will help take you through the training process for so many aspects of dog ownership and answer many questions.
You can download the book
here. Let us know how this technique works!