I can totally empathise with you. I have a toddler daughter too and I worry about her constantly. Like, constantly! Becoming a mother has aged me 100 years I think sometimes.
I have HA and GAD, and I do worry about my own health a lot. But now that I have my daughters health to worry about too, it's even less fun. She wasn't even ever sick til she was about 14 months. Once she had a rash and I couldn't get it to blanche so I rushed her to the doctor, who straight away got it blanche. I was a wreck though thinking it was meningitis. Then at 14 months she got sick for the first time with tonsillitis. A few weeks later it was gastroenteritis, then tonsillitis again, then a post-tonsillitis cough which irritated her tummy and made her sick. Now she has a high fever and some vomiting and my nerves are shot! ANy time she is sick, I set up her travel cot in my bedroom so that I can keep a close eye on her during the night. It must be very tough letting her go to her Dad's. Are you on good terms with him? Can you ring him to ask questions about how she is? I am married and although my hubbie is great, I would not trust that he would do as good of a job as me looking after my daughter when she is sick. I'm not sure if other mothers feel the same. Maybe it's a natural mother instinct thing, maybe it's Mammy anxiety.
Reading this back, I'm not sure what I'm saying will help you as I had intended. But know that you are not alone.