I had a "sea lice" outbreak once on a cruise, and it was unpleasant, but not life-threatening. It was basically like a bad rash. I didn't go to the medical center. I just took some Aleve and was uncomfortable for about a day. A bad jellyfish burn could require some medical care, but I'm pretty sure Disney has nets to keep out any big jellies. "Sea lice" are microscopic jellyfish larvae, and they aren't that likely to fire their stinger against exposed skin, as I understand it. The problems come when they get stuck in between the swimsuit or swim shirt and the skin, and then die because of friction and pressure or because of showering in fresh water. So it's important if you use Safe Sea to put it under the bathing suit.
My rash was like the one in the picture in this article, but much less severe and covering a smaller area. And mine lasted for maybe 2-3 days, but was only really bad for the first day.
http://www.nola.com/health/index.ssf/2016/06/sea_lice_florida_coast.html
I'm sure you could use some kind of numbing gel or cream to treat it, just like a sunburn, or that article mentions antihistamine and hydrocortisone creams. Or the Safe Sea people now have an after-sting relief treatment; that would likely work, but I've never tried it.