My daughter gets those every time she gets her hands on makeup. she's allergic to them and ends up with styes always.
We have never had to drain them. I am very consistent with warm compresses and eye cream and drops once she gets them. I heat the compress in microwave for about 15 seconds (wet it first) then put it in a ziploc bag. wait until your child is ok with the warmth and then hold it for at least 8-10 minutes. do this as many times as you can. I do them every 2 hrs. yes, it's an overkill but my daughter knows (she is 6) that we either do it often or she may have to have it drained (she does not like doctors so she opts for this). We also put the cream and/or drops that the eye doctor prescribes. To put a timeline when does it disappear? after doing this regiment constantly throughout the day, it goes away within 10 days to 2 weeks. yes they last a long time but eventually go away. the longest that stayed was the entire summer (2009). no matter how long we did the compresses, it didn't matter. we dealt with it for an entire summer.
ps i didn't use tea bags or anything of the sort. just warm compress and whatever the eye doctor prescribed.