Not your fault at all, don't beat yourself up.
I know how you feel, as my DS did the same when I took him to a series of antenatal classes with other mums and babies. They had a series of people to talk to us and no matter what I did, my DS was the only one to scream the place down - I tried walking around with him, feeding, changing, cuddling: nothing worked, and you feel like everyone is looking on and thinking you are hopeless, and pleased it's not their baby doing it, but they aren't at all! I even didn't go one week because of it. When I took him into work for the first time, he did it again and one of my colleagues ( a mum herself) took him and walked round with him and he stopped! I felt completely hopeless, and in all cases, as soon as I put him in the car and started driving he dropped off to sleep immediately - so why didn't he just quietly go to sleep in the event!?
Have you got someone from NCT that you could invite round and have a chat to? With a first baby everyone has something they aren't sure about, and sometimes asking what other people are doing can help. I had only just moved to the area when I had my DS and didn't know anyone either, as well as being quite shy, so got together with a couple of other mums and pooled our ideas on weaning etc. Really helped. Have you got a nice health visitor? You could ask her round for a chat too.
Hope you feel better soon, but you definitely aren't a bad mummy.