Per guidance from health agencies, your child should STAY HOME sick from school if they have these symptoms:

• Respiratory illness (cough, runny nose or sore throat with a fever).
• Signs of severe illness such as being unresponsive, irritable, crying more than
  usual, is having difficulty breathing, or has a quickly spreading rash.
• Fever (temperature above 101°F [38.3°C] by any method) and a change in
  behavior or other signs and symptoms (such as a sore throat, rash, vomiting or
  diarrhea).
• Diarrhea, defined as having more frequent and loose stool (poop) than usual
  that’s not caused by a change in diet.
• Vomiting 2 or more times in the previous 24 hours. The exception is if the
  vomiting is found to be caused by a non-infectious condition, and the child is not
  in danger of dehydration.
• Abdominal pain that continues for more than 2 hours, or abdominal pain that
  comes and goes, along with fever or other concerning symptoms.
• Mouth sores that are open and draining, unless their doctor or
  local health department authority states that the child is noninfectious.
• Rash with fever or behavioral changes, until a primary care provider determines
  that the illness is not a communicable disease. If your child has a new, rapidly
  spreading rash that resembles bruising or small red or purple “blood spots,” call
  911.
• Skin sores that are weeping fluid located on an exposed part of the body that
  cannot be covered with a waterproof bandage.
• Streptococcal pharyngitis (such as strep throat or other streptococcal infection),
  until at least the first 12 hours after antibiotic treatment has started.
• Head lice, scabies and ringworm until after the first treatment. School exclusion
  is not necessary before the end of the program day. When treatment starts
  between the end of the program day and beginning of the next day, no exclusion
  is needed.
• Chickenpox (varicella) until all lesions have dried or crusted (usually 6 days after
  onset of rash) and no new lesions have showed for at least 24 hours.
• Hepatitis A virus infection, until 1 week after onset of illness or jaundice or as
  directed by the health department.
  

Per guidance from health agencies, it’s okay to stay at school:

• Coughs or colds without fever or other signs of illness.
• Runny noses (regardless of color or consistency of nasal
  discharge).
• Yellow, green, white, or watery eye discharge without fever,
  even if the whites of the eyes are red (pinkeye).
• Ear infection, unless the child has a change in behavior or
  cannot participate as usual.
• Rash without fever and without behavioral changes. The
  exception would be a child with a new, rapidly spreading rash
  that resembles bruising or small red or purple ‘blood spots.’ In
  that case Emergency Medical Services (911) should be called.
• Thrush (white patches on the inside of the cheeks, on gums, and
  the tongue).
• Fifth disease (a common viral infection with red “slapped-cheek”
  rash occurring 4-14 days (up to 21 days) after the start of the viral
  infection).
• All staphylococcal infections. This includes Methicillin-
  resistant Staphylococcus aureus (MRSA) carriers or children with colonization of skin MRSA but without an illness that would otherwise require exclusion. Site must be covered at school.
• Hand-Foot-and-Mouth disease. No exclusion is needed unless
  the child has mouth sores that are open and draining or has
  other symptoms like fever. In some cases, the local health
  department may require children with hand-foot-mouth disease
  to stay home to control an outbreak.