Thanks for your query.
You and your child have stye
, which results from an infection of the oil glands of the eyelid. commonly it is caused by staph. stye can be contagious and spread bacterium to others So keep your eyes and hands clean, and don't share pillowcases, bedsheets, washcloths or towels with others.
You shouldn't pop a stye like you would a pimple. Allow the stye to rupture on its own or visit doctor to drain it.
Hope it helps.