Kitten (5 wk old) with blood in diarrhea?

Just over a week ago I took in some foster cats: a mom and five kittens who were roughly five weeks old. One of the kittens (Rosey) was not part of the litter; she was simply found on the street and came to me with really bad sniffles/wheezing. I've been using a humidifier with her and mom is on antibiotics for the cold as Rosey ped it on to the rest of the cats, so these should stop any secondary infections via mom's milk. Although the sniffling hasn't worsened, it had not got better for Rosey and she has had diarrhea for the past few days and stopped using the litter tray. Today the diarrhea turned to a brightish green slime that she seems to have no control over releasing and I spotted a patch on the floor that had a tiny, tiny streak of blood in it. She is still eating, although she didn't seem interested in canned food just a few hours ago. She is still nursing regularly, however, and laps up water when I put her near the water bowl. The cat rescue place say I should just keep an eye on her for a few days, but I am not sure whether they are saying this to avoid vet bills (which they are meant to cover) and I cannot afford to take her to the vet myself. I did recently change the canned food I feed the kittens to a different brand so I wonder if it could be that or if it could be as a result of the antibiotics. Either way, I am worried because I've read things on the internet about dehydration from diarrhea killing kittens quickly. She seems to otherwise be in good spirits.