I'd never heard of chiggers before: eugh! However, this has always happened in urban areas (Mississippi, North Carolina, Louisiana...), which seems to rule them out? Thinking about it, this didn't happen to me last time I was in the US, but on the West coast.
... That said, I react very differently to mosquitoes around the world, and what you're describing sounds like what southern European mosquitoes do to me (although the wheal is 8-10 centimeters at its largest and it takes more than a week for the bruise to go away.) For comparison, US mosquitoes cause a mildly itchy spot for 6 hours max and then slowly disappear into little pink spots.
That's interesting. The bite you get from mosquitoes in the US is how I react to bites in the UK. I think that mozzies are the most likely culprit.
Are you using bug spray? Might be time to step up to stronger stuff, if you are.
<<<head smack>>> Why didn't I think of that?! No, really, I've never tried it. It's not something I've ever needed before. I get bitten by a mozzie perhaps once or twice a year at most so it's never been an issue.