Totally sympathise. Holidays and children being sick are really really difficult when both parents work out of the home. I thought I was going to get an ulcer with the stress when my two were little..
I certainly remember times when me and my husband have had the 'who's job's the most important' conversations.. (I say 'conversation' loosely - I'm sure the neighbours heard the 'conversation' on occasion!).
Things do seem to come in cycles, and you can often find yourself with a 'too poorly' for nursery child a lot at this stage. Hopefully when the winter is over things may settle down.
Will your nursery give Calpol? If not, have you asked your GP to give Calpol on prescription? This was a godsend for us when DC's were 'under the weather' but chirpy on Calpol.. the nursery wouldn't give it from a Boots bottle, but will give it if it's prescribed (fair enough). Both DC were fine at nursery with Calpol when just generally snotty / teething / slight temperature.
(You can also keep a prescribed bottle and wash it out for future use... you never heard that from me
!).
Failing that, if a nanny is not an option, a friend of mine used to use a lovely, older neighbour. The neighbour wasn't up for any form of regular sitting, but was quite happy to have a little one of the sofa for a day if they were not themselves...
Don't feel alone - although you may be thinking about giving up work, are work actually making you feel bad, or is it coming from you? Can you work from home? Can you stagger your hours? You're definitely not the only parent with this problem, and now mine our older the odd sick days seem much fewer and far between xxxx
(where's the 'don't jinx self' icon when you need it?!!!)