A fever is only one symptom. Look up various illnesses so that you know the other symptoms. For example: the throat is very red with a strep infection. And the throat hurts too bad to swallow. My granddaughter also gets very lethargic. The only way to know for sure if it's strep is with a culture. The school nurse knew it was strep and the culture taken at the doctor's office confirmed it. I suggest that with experience you will begin to recognize symptoms.
Ear infections usually are recognizable when the child pulls at his ear and if old enough to complain, complains of pain.
I suggest that keeping your child home and wait to see if (s)he improves is a reasonable thing to do. The medical community is finding that it's best to use anti-biotics as seldom as possible. If your child is improving after a few days they didn't need the anti-biotics in the first place.
With a school age child, my first thought is always what is going around at school. Most likely she has what other children have already had or are having now. You can call the school and ask what is going around illness wise.
Vomiting a tablespoon of fluid is no reason to be concerned. A sore throat is also typical of common viruses. You're doing the right thing. I know it's hard to wait and see but if you took her to the doctor he would tell you that.
A serious illness will manifest its self with serious symptoms that you can't miss. One of those is a high fever, even with your children. A strep throat and an ear infection are not serious unless the child stays obviously ill for over a week. I've had strep throats that I didn't go in for a diagnosis for until the second week of soreness because I could still swallow fluids. It's dehydration that is the main concern.
It's chronic ear infections with a high fever that cause concern.
I suggest that your children are normal and the degree of fever does indicate how ill they are. They will not be harmed by your waiting to see if they get better. If they continue to get worse, that is the time to call the doctor's office and ask about it. They will have you come in if they think it's helpful.
I've had colds and sore throats that have lingered for weeks. Most of my friends have had the same experience. We finally go in and are told, "it's a virus. "There is nothing I can do for you. Continue to drink plenty of fluids, get rest, take ibuprofen or Tylenol for the aches and come back if you're not better in a couple of weeks." I have gone back and been once again told the same thing. The only time the visit was different is when I had mild congestion in my chest and he diagnosed walking pneumonia. I think I took an anti-biotic for it. Usually, I've been told that the anti-biotic is to prevent me from getting a secondary bacterial infection. I think my pneumonia was still considered to be a virus.
Continue as you are doing. Keep them home, resting, and drinking plenty of fluids. The pediatricians I've had experience with have all said that they are usually not concerned when a fever is less than 102 or so when the child is school age and only has cold or flu symptoms or it lasts longer than a few days. Always call, tho, if you're concerned.
My daughter and now my grandchildren were rarely ill longer than a week. They were usually well enough to go to school by Friday and then I was faced with the decision of whether or not to send them, which is another post. :)