My cat is very sick!!!

My cat (let's call him N) won't eat or drink, he vomits a lot and one time there even was a worm. He also has diarrhoea. Last night his condition got so much worse. His nose and mouth is bleeding, he's having trouble with breathing through his nose. All these happened in just one day. We took him to the vet, they gave him some shots, but still we don't know what this disease he's having. All we know is that this is a contagious disease as he got this from our other cat M which had the same symptoms (except for the bleeding and diarrhoea). at first we didn't know M had serious disease, we thought it was just anorexia, so we didn't isolate him from N. unfortunately he died 4 days ago. 

Now we're worried sick, we don't know what to do. It pains us so much seeing him suffering like this.

Oh, this isn't good. I am not an expert, but to me this sounds like feline parvo, or panleukemia.

It is very contagious and almost certainly fatal without aggressive treatment. I am so sorry. Was your cat vaccinated?

Please, if you can't treat your cat, regardless of what this is, please do not let your cat suffer.

Here's a link. Again, I'm not an expert but it does sound like it.
https://en.m.wikipedia.org/wiki/Feline_panleukopenia

Poor cats

Please take your cat to the veterinarian again ASAP. It could very possibly be panleukopenia as suggested by @misterwhiskers, and even without a proper diagnosis, your cat needs supportive care. At the very least call your vet. He or she checked the cat and need to follow up on him.