What's biting me?

I got one bite, then a few days later a second. Then a third. Finally after a month I have about 10. They're the size and shape and color of mosquito bites, except they have a little hole at the top that sometimes leaks a little clear fluid. Eventually it becomes a little scab, and it takes about 2 weeks for the bite to disappear. They only occasionally itch. They're on soft tissue (chest, stomach, bum, thigh, behind the knee). They started right when I moved to a new place. I notice that there are a lot of little spiders outside, but it seems hard to believe since the bits aren't around my arms, feet, etc. There's a cat so a possibility of flees? Bed bugs? The bites aren't in a string, they're just one by one, a new one every few days. Or could this be something else? Not bites at all??