Cat has fleas- help!!

[Bailey20]

My cat has had fleas before, and I've got rid of them pretty quickly, but I've just found them in my cats bed. She won't let me search her, just keeps running away. Thing is I have a 4 month old DD- I hate fleas enough anyway as I'm allergic to insect bites but now I'm worried they'll get on my DD and bite her. What is the quickest and most efficient way to get rid? I've already put all of the things the cat sleeps on on a hot wash. TIA

You need a decent fle treatment for the cat. I've heard on hear Advantage is the only non prescription one which works Otherwise you need something from the vet and keep on top of monthly treatments.
We use Stronghold and have used Advocate in the past with no issues.
For the house Indorex.

Don't you use a monthly flea treatment? One from the vet not over the counter.

Advantage , definitely . Our middle cat is a flea magnet and this stuff works .

Second for Advantage. No prescription needed.
I recently bought some from Pet Drugs Online and it was less than £12 including postage. Arrived the next day and there were three or four treatments in it, so should see us well into the year.
Worked a treat and really quickly!

Thanks for all the suggestions. Yes we normally go to our vets for treatment so no idea how this has happened as she's not due a treatment.

I get broadline drops from the vets, to take home and I apply them to the back of my cats neck every month. They prevent fleas and ticks.