If you have a major flea infestation, you need to treat inside your home, outside your home and all pets. I suggest you look up how to get rid of fleas and you can read up on the steps you have to take. You may have to biomb your house, taje any pets out and treat them before you bring them back in. Vacuum everything you can and get rid of the waste in the trash. All dog bedding should be thoroughly washed. You should check with your Vet about a monthly or topical medication to put on your dog.
Yes, I would think a good topical (perhaps Advantix) would begin the process, as it kills the fleas plus their eggs. If they can't 'feed and breed', they can only diminish. And as Margot said, treat the yard and the house. Boric acid on any carpeted area should eliminate most, if not all. Once you break their reproduction cycle, you should see a reverse.
Just a note, many dogs have had reactions to OTC Advantix. Not saying that would happen, just something to be aware of.
Yes, many dogs can have reactions to many things. What can you do?
A first time dose should be at 1/2 the recommended for that reason. If OK after 24 hours, should be good to go. If no reaction, fleas go to dog, fleas die. They only reproduce after feeding, and even if they get to the feeding part, they will be dead before they can lay eggs.
As for 'bombs'.....people and pets both will be breathing that insecticide until it clears the house.