Chiggers would not come from the pool area. I have had a case of them that infested my whole lower body with over 350 bites, etc....so I did a lot of research. Topical ointments will help relieve the effects, but really they run the course. Usually by the time you realize you have them, it is too late to do anything about it and most "remedies" will only appear affective as the chigger finishes its business.
Chiggers are a miniscule mites about the size of a pinhead, usually you can only see them after the welt appears and they are just a small spot in the middle of that welt. They must bit a mammal in order to move from larvae to nymph. After they feed on a mammal to make this tranistion, they actually turn vegetarian...and will not bother anyone again (so you don't have to worry about them being in the house, etc). They will normally become highly concentrated in an area that is not frequented by mammals...swampy areas, heavily wooded areas, deserted beach area's, etc.
For the OP, if your have been in one of these areas about 24-48 hrs before the bites appeared, that will narrow down that it is likely chiggers....the bites might get worse (more numerous) as you react to them. It took about 24 hrs for the first bites to appear on me and 48 before the final ones...then about 72 hrs for things to subside and heal.
If you have not been in these type of areas....you might want to make sure it is not bed bugs from the room. I would not suspect any Chiggers in the WDW area, unless you are in an area not normally visited by the public or other animals (say a "shortcut" through the woods, etc).