Oh, dear. We just got rid of a huge flea infestation. We agreed to watch our daughter's cat for her this past summer while she moved and vacationed. We had her for almost a month and she had fleas, but we didn't know it. She was even confined to a bedroom and we did let her upstairs during the day, so she had eggs falling off of her like crazy. The infestation grew before we even knew we had fleas so we probably missed an opportunity to try to eradicate the problem before it got out of hand.
You can try this: start vacuuming your entire house and all of the furniture. Wash blankets and pillow coverings if you can and if the cat has gone into your bedroom and gotten close to any beds, take those sheets off the bed and wash in hot water. DO NOT flea bomb the house. What you buy in stores has chemicals in them that can possibly harm you and your animals. I don't know if you have Borax where you are, but if so you can sprinkle that on your carpets, rugs & furniture (first vacuum, then sprinkle the Borax). Leave on for a couple of days, then vacuum again. Make sure to get rid of the vacuum bags after each vacuuming session so that the fleas don't hatch inside the vacuum bag and reinfest your house. Seal the bag in a garbage bag and dispose of outside away from your home. The Borax is supposed to dehydrate the fleas & eggs so they die.
You can also look for flea spray to use on the furniture and spray on the carpets/rugs. Try to find one that contains an insect growth regulator. These will kill the fleas and prevent the eggs from hatching. If you don't have Borax, then look for a flea powder for carpets that includes an insect growth regulator and sprinkle that on the carpets, rugs & furniture and leave on overnight, then vacuum. But remember before you treat, vacuum first then treat.
You also need to buy Frontline Plus and use on the cat and use Advantage for your dog. It's a liquid that you put on their necks and you do that every 30 days. My vet told us that since we had an infestation, we could re-treat every 21 days until we felt the problem was gone, then we could go back to the 30 day treatment.
You also need to vacuum every 2-3 days and repeat the process of washing clothes, blankets, sheets, pillows, etc. because eggs drop everywhere and can hatch inside of clothing, etc. It's truly a pain in the butt to try to get rid of the fleas, but if you don't have a bad problem right now, you may can get rid of them yourself.
Try this for the next couple of months and if it doesn't work, then you will have to call in a professional to come spray the entire house. If you have to do that, then be prepared to leave your home and take all of your animals with you (including other pets like fish, etc.) because nothing alive can be in the home while they are spraying and you have to stay away for 3-4 hours. They should also offer to come back and retreat in 7-10 days and you have to vacate again. We had to do this and it was SO worth it because it killed our fleas and we haven't had a problem since. We are still treating our three cats with Frontline Plus and it seems to be working. I haven't seen any fleas since they came out and sprayed in December.
Good luck to you! I hope you can get rid of them yourself so that you don't have to pay a professional, but if it comes down to it, then paying the professional will be well worth it.