You know we went through the very same thing when my son was 10 months old and moved into full time daycare. They are really clean there, and even have heated floors with no carpeting. Carpeting is a germfest. He was sniffly all of the time, had hand, foot, mouth a few times (different strands) and pink eye twice. But it was a good place, we could afford it, and I just took as one of those things you have to get through when the going gets tough. Seeing as how your daughter is about the same age as my son was, it seems like it's one of those crappy phases we have to go through.
If you have another daycare that you think you can make work, give it a look if it makes you feel better. I can tell you my son is 4 years old now, at the same daycare, and has had only 1 ear infection, hasn't had a sore throat once, has never vomited, and hasn't really been "sick" in years. (knock wood)
I know it's tough to have to work and not have a lot of control over situations like this. It's like you never get a break, right? You pay for it whether they are there or not. They don't always do what you would do. Your kid gets sick at the worst times, and you are going through a tough time. Take things one step at a time and things will fall into place. I think looking at all of your daycare options might make you feel like you have a little more control over it all. If you find one that you can afford and send her to and her health improves, that's great. If you find this place is your best option, then you can just take it from there.
I have been there, just keep breathing and do your best. It will work out!
xoxo