You have mentioned pain in left side but not mentioned which part of the body, is it stomach, leg or entire body pain
Since you have said she vomited i assume it is a pain of abdomen.
for a 10 year child may be due to worm infestation, or muscle spasm. there is also a chance of infection (as in food poisnoning) often there wouldnt be fever
. There is no evidence to suggest Urinary tract infection
You may get her anti-spasmodic and give antiemetic if vomiting
Ask for any new food she took from her school. Or enquire her teacher for this history. like kind of food stuff, cooked or uncooked, tinned or not. refrigerated etc
If you find something out of ordinary get her to a paediatrician, he may able to provide appropriate antibiotics to your child
Hope I am of some help