There is a medication called "Stye". I'm not certain if it can be used on a toddler, so you might want to check with the pharmacist. I normally can find this at Walgreens or CVS although you might have to ask one of the pharmacy techs to help you find it. (It's in a really small tube and doesn't have any flashy packaging to make it stand out.)
Make certain hands are being washed and everything touched is being sanitized- doorknobs, phones, faucet handles.
If the stye doesn't go away after a couple of days or develops a crusty film, take the child to the doctor or a walk in clinic- I know the one in Acme Grocery Store saw my husband for a stye with no problem (we thought it might be pinkeye).