People saying that it is none of your business @mylittleyumyum
are, in my opinion, part of the problem that so many countries, including ours, have these days. I very strongly believe that where babies and young children are concerned, every single one of us should ourselves be concerned to keep alert to the welfare of any children that we ourselves are aware of in our daily lives.
By that, I don't mean be a curtain twitcher, or embroil yourself in other peoples lives, but just be aware of things like the OP is asking about here, or if you hear lots of shouting, and maybe a child crying and/or screaming in a way that makes your stomach and heart feel very heavy, and/or tight, and/or nauseous, or even makes you feel scared for anyone vulnerable in that house.
If they are putting their baby into cold damp bedding, then yes, OP that could easily be the reason for the baby being so unwell. Have you ever been inside their house OP, or at least since the baby was born? If they are suffering from damp problems inside their house that could easily lead to breathing difficulties in the child as well. Do you happen to know if anyone in their household smokes indoors OP, as that, of course, could also lead to breathing problems?
Have you got any idea about what the parents are like, and whether they can afford to have their heating on during this awful weather? Do you think that at least one of the parents is intelligent enough, or has enough common sense, to know the main basic aspects of bringing a child up, to know whether they probably already know how to bring up their baby as safely as possible. Sadly, of course, any of us can, and many of us probably have, made stupid, or even bad mistakes, as we are all - at the moment - still humans...
You might not know any of the answers to the questions I have asked you about, especially if they keep themselves to themselves, which is of course their right. I am a very private person myself, so I understand about not being happy with other peoples interference in my business. However, if I had ever done anything potentially harmful to my children, I might have been very embarrassed, and maybe even cross initially, but in the end I would have been very grateful that I had been advised by someone - preferably someone professional - about the potentially harmful behaviour etc. You do seem to have some genuinely serious concerns OP, and if they are not the sort of people who you believe would welcome an 'almost stranger's' advice, then I think you should contact someone in authority, with the hope of them being able to carefully give some very useful guidance to the parents about essential practices with babies and young children; but obviously, not with the aim of getting them into trouble.
Of course, I would have hated someone I hardly knew, offering me advice when my children were younger, but I was very lucky to have a brilliant Mum, and I could have also asked my family doctor for advice (in those days). I also read various books about child rearing during my pregnancy, and while my first born was still young. In the early years of my first baby's childhood, I read a book about the first year of a baby's life, by a lady called Penelope (damn, I have literally just forgotten her surname, but it might have been 'Leach'?), and I agreed, almost instinctively, with almost everythin̈g she said, some of the other authors, not so much.
Unfortunately @mylittleyumyum I know next to nothing about what professional advice is available to new parents these days, but this site must be full of those who do, who can advise you about which is the best service to contact for advice, and to hopefully do maybe a 'routine check' on the family's welfare. Good luck OP, and Thank You on behalf of all of us who do still believe in "The Village". 🌻