understandable!
especially with your first - which she is, by the sound of it! 
a good way to avoid being neurotic about things is to observe. to look at what actually happened.
write it down so you can read later, when not so emotional or worried.
but if in doubt definitely listen to your gut instinct above all else! your child, your decision and you have to deal with the consequences!
that served me well so many times before, but one event sticks out. we were on a holiday at a friends house and were due to leave after lunch on the Thursday, day before Good Friday (therefore 4 days without GP)
our three kids were all sorts of coughing, sneezing, raised temperature etc riddled by Wednesday morning, so I told DH that we should leave that evening so I can take them all to the doctors in the morning.
he said why should we cut our holiday short, they will be fine and anyway it's not very polite to leave earlier...
I told him that he can either drive us home or I'll get a cab, but we are going.
so we did, cue GP's vist the next day with the result of DS1 - tonsillitis, DS2 - viral throat infection, DS3 - ear infection.
I was "victorious"!
I knew it, I knew they were ill! I told him that I will not say "I told you so" but I never, ever want him to doubt my tiger mother instincts. ever.
And I'm so glad I was not swayed by anyone's emotions or reactions or anything.
I hope this helps!