I too suffer with emetephobia.
I am also a trained and qualified Nursery Nurse / former Nursery Manager.
Illness is unfortunately part and parcel of sending your child to Nursery and they do get unwell whilst building up Immunity.
However... a few things that's REALLY important on your part:
Always ensure thorough handwashing when your child gets out of Nursery and comes home. This is where the majority of virus' are transmitted- fingers to mouth route.
Sounds over the top to others but being an Emetephobe , I would shower my two when they got home from Nursery. I found it a win win; they'd be clean and ready for bed, as well as the germs and yuk from Nursery had gone.
Thankfully, my two children never once picked up a sickness bug from Nursery in the times they were there.
Also, observe and read the Nursery policies and procedures and don't be afraid to ask questions . All staff in Nurseries should be strictly adhering to hand washing/ cleaning routines. Both for the children and for themselves. For example, washing hands properly before eating food/ coming in from outside etc
Especially with Covid one would hope these measures are ramped up significantly.
Ask about the illness exclusion policy. Is it adhered to when the children are unwell with sickness and diarrhoea? Many settings will say, oh yes, absolutely it is followed, when the reality is that they do allow the children back into Nursery before the 48 hour exclusion period for sickness and diarrhoea is over. Not all settings I may add, but definitely some.
This can be for many reasons; often it's that the Manager is not very strong in their leadership and doesn't follow it through fully or it could be for financial reasons as well. In my experience, I have often found it is actually down to the parents too as because they are often paying for the service, there will be a few who will lie over their child being unwell.
You need to be prepared for this as sadly this can happen a lot. Many parents do indeed tell lies and now I work on the other side of the fence ( and visit many Nursery and School settings for part of my job) it is indeed commonplace.
Ask too about staff turnover, as this a good sign that things are well run.
Good luck with your choices but please do not be afraid to ask questions.