Have you spoken to your landlord so s/he can get a pro service in? I remember years ago someone I worked with told me she used mothballs in vacuum bags. Their cat had gotten outside and ran off for a couple days. She said it brought fleas back. Anyway, she kept putting mothballs in her vacuum cleaner bags. Can't remember specifics now, but I want to say she did this for awhile, like a couple weeks, and vacuumed a lot, like a couple times a day. I guess the theory was they got vacuumed up and mothballs in the vacuum bag killed them. I would think those vacuum bags would have to be thrown out after each time vacuuming, and outside somewhere in a garbage can, not inside. (She claimed it worked, but you might want to google that. And for sure be careful with baby, mothballs would not only smell when vacuuming, but also look like candy to a child, so exta care would be needed.)

Meantime, your little one is suffering, and multiple bites like that aren't good. Your LL has a responsibility to take care of this. And don't be afraid LL is going accuse you of having sneaked a pet in or something. Fleas can get in a lot of ways other than a pet. Rodents can carry them in. So if you've seen a mouse or evidence of one, perhaps get some traps and put where baby can't possibly get to them.

It might have something to do with the life cycle of fleas. There's a stage where the eggs are dormant. You can bomb and kill the adults, but the eggs will hatch a week or so later and you have fleas again.

I'd see if the landlord can do anything.

And moonshadow's vacuuming tips are spot on. Vacuum and then immediately discard the bag outside. You might try vacuuming floors and any upholstered furniture daily for a week.

If you've got carpeting, that where most of them are. And if your baby is playing on the floor, she's right at their level. See if you can keep her on a hard surface to play until the problem is under control.

Breaking you lease should be your last option because you'll likely loose your security deposit and it could have an impact on your credit rating making it harder to get another apartment. There are acceptable reasons for breaking a lease (such as a pest infestation) but you need to notify your landlord and give him a reasonable amount of time to address the problem. If he isn't responding to a telephone complaint, you should send him a letter via certified mail with a return receipt so that you have legal proof that he was notified of the problem.

As others have mentioned, any kind insecticide will likely require at least two applications. One of kill the adult fleas and one to kill any eggs that hatch in the future.

Go to your local vets they have a spray that works..Bombing often does not work as it can not get under all the furniture

If you haven't seen any are you sure they're fleas?

Sounds more likely to be bed-bugs to me...