Unidentified bites!

My wife and I adopted an adult dog about a week ago, and since he arrived I've been getting small itchy bites on my arms and legs. Some of the bites are small and round, others are more elongated, like there are two bites next to each other. At first they showed up in groups, but the last day or two it has only been single bites. I scratched one grouping of bites a bit more than I should have and it turned into a large (one inch wide and two inches long) ugly red welt that has persisted for several days. The bites have only been occurring on uncovered areas, and I usually only notice them in the mornings. I know it is not fleas - I've lived through a flea infestation before and can recognize the bites easily. Also, the dog is up to date on his flea treatments. I've seen absolutely no sign of bedbugs, either. I'm not allergic to dogs, so I don't think it is hives. My wife got a couple of bites at first, but they didn't itch and she hasn't gotten any since. We've washed our sheets in hot water and have been sweeping, mopping, and vacuuming like crazy, but the bites keep coming. Any ideas as to what could be biting me?