We JUST went through this a few weeks ago. The fleas are really bad here this year (and last year) because we've been in a drought and they seem to thrive in this
First thing is to get the fleas on your baby. Get something from the vet to put on her to repel and kill the fleas. Get her out of the house for the day, get someone to watch her, even if you have to pay the vet to board her for the day.
Then the fun begins. I finally found a flea spray that works, it's called Enforcer Flea Spray for Homes. I got it at Home Depot. Remove anything washable from the apartment and start washing it all in hot water and dry it on high heat. Do not bring anything back to the apartment until you have killed all the fleas. I don't know your laundry situation, so this may be difficult for you, but if worse comes to worse you can seal all the clean things in big garbage bags if necessary. Wash EVERYTHING, including her beds and soft toys. Fleas lay eggs everywhere! Spray everything that it not washable, like the furniture, mattresses, etc. Make sure to get under cushions, under the furniture, baseboards, and the floors. Get out of there for a few hours. When you return, open all the windows and run some fans/AC for a few hours. Mop the hard floors with hot water and vinegar to remove excess pesticide residue. Don't bring your baby back in until you are sure that it's all dry. It's a lot of work, but it's the ONLY way to get rid of the fleas.
Now the yard. Since you live in an apartment, contact the landlord and ask them if they will have the yard treated. In the meantime, carry your baby down the street to a different yard, if necessary. I'm lucky that my girls are pee-pad trained, so I didn't have to do that. I just didn't let them outside for a couple of weeks, until I could be sure that the treatment I used on our yard actually worked this time
It took me going through this process THREE TIMES to finally get rid of the little buggers, GAHH!! My littlest one even got a skin infection from scratching so much
They are both allergic to fleas, and your baby might be too. A lot of them seem to be. In that case, the itching might continue long after the fleas are gone. If you're sure that the fleas are gone and the itching persists, ask your vet to give her an anti-inflammatory shot (which will stop the itch cycle) and check her skin for any infection.
Oh my good luck, I hope you beat the little buggers, they are SO hard to get rid of and will test your sanity
Also be careful when you come into the house, as they can come in on your shoes and start it all up again. If the landlord won't treat the yard, you may have to do it just for your own sanity and convenience. Maybe other pet owners in the complex will share the cost/labor with you?
Thinking of you and NOT envying the work you've got ahead of you. Hang in there!!!