Most spider bites are harmless, causing redness and swelling at the site but no serious risk, so you can probably relax. Wash the site thoroughly with soap and water, and apply an ice pack or ice cube to reduce any swelling and redness. If it hurts, give your child acetaminophen or ibuprofen as needed. The swelling and redness should go away in a day or two. The only spiders that pose a real danger are black widow and brown recluse spiders.
Black widows are shiny black with a red hourglass mark on the belly.
Scorpions are also potentially dangerous. If you suspect that your child has been bitten by a poisonous spider or stung by a scorpion, put an ice pack on the bite and take her to the nearest emergency room where a doctor can give her an injection to neutralize the venom. If the spider was poisonous, your child will be in intense pain within a few hours. She'll also have severe muscle cramps and possibly sweating, vomiting, tremors, and difficulty breathing. Without prompt medical attention she could go into convulsions and even die.