STOP. You are going to be OVERTREATING your home. Frontline or Advantage monthly applications ARE ALL YOU NEED TO PUT ON YOUR CAT. SOmetimes bathing in flea shampoo can cause more problems than they treat. Any fleas on your cat will die due to the monthly treatment. Put the pillow in a hot water wash, put some powder in the vacuum cleaner and clean all the surfaces in your home. The fleas you suspect you have should be gone, do this again in three days and again three days after that to kill any eggs. You can also use Diatomaceous Earth in the cleaner. Just dont use the kind you use in a pool (it has extra chemicals in it) good luck

I don't know what kind of powder you would put into the vacuum cleaner, but I would not recommend this. The air coming out of the vacuum will carry residual powder which you will be breathing.

Frequent vacuuming of the carpets and especially of the chair (in the cracks and everywhere you can go) should take care of any fleas.

Just use the anti-flea stuff on your cat, then thoroughly vacuum the chair -- all the cracks and crevices.

The reason is this:
Flea eggs drop from the adults.
Eggs land in cracks and crevices.
Eggs hatch.
Larvae eat debris, much of it droppings from adult fleas.
Later -- maybe several weeks -- adults emerge and can bite animals and people.

Beyond that, comb your cat daily as a means of monitoring the numbers of fleas s/he has. (No, you won't get them all, but you'll have a good indication of the population trend.)

Oh yes, you need to know that foggers ar a waste of time and dollars.

They don't expel a true fog which penetrates cracks & crevices. Instead, it's minuscule particles that are flung upward, then fall down.

I agree with mazer, socks and jean. Not sure about the diatomaceous earth in the vacuum cleaner, but know that eggs sucked inside will hatch, so I would empty the vacuum in the trash outside after each cleaning.