Before you put it down to fleas, please please check for bedbugs.
Bites are too variable to determine whether you have bedbugs or something else. Some people don't react at all, others get blood filled blisters - and everything inbetween.
You need to lift up your mattress and look in the underneath seams, buttons and around the edges of labels. Look at your bed frame too, paying close attention to the joints, screw-heads, ends of slats etc. They like little nooks. As well as live bugs, look for cast skins and faeces, which looks like little black dots (see image). If you have a divan turn it upside down and take off the underneath fabric. They like divans.
If you have the slightest suspicion you might have bedbugs you should check for them before treating your house for fleas because bedbugs are resistant to pretty much all pesticides, at least those that are licenced in the EU, and what doesn't kill them pisses them off and drives them into your walls, under your floorboards, into other rooms in your house and it will take much much longer, and much much more money to get rid of them.
Treating your cat for fleas is fine but check for bedbugs before spraying indorex or any other pesticide around your home.
Good info on bedbugs here:
bedbugger.com/2007/01/20/faq-think-you-have-bed-bugs-some-dos-and-donts/
u.osu.edu/bedbugs/