Congratulations on your new, furry addition!
I'm sorry that she came to you with fleas. She is old enough to be started on a monthly topical flea treatment, sold by your vet, like Advantage, Frontline, etc. Since you have an appointment for her with the vet, tomorrow, wait until then to discuss this with him and ask which flea treatment he would recommend. Of course, you would need to get the kitten version of whichever treatment you and your vet choose. Since you've already used the Pet Lock on her, tell the vet and you might not be able to use another topical flea treatment for a few weeks. I hope she didn't develop any adverse reactions to the Pet Lock.
It's safest not to use any flea treatments sold in supermarkets or pet stores, as they are not effective and have been known to cause serious adverse side effects, some even fatal! The biggest offenders are HARTZ, SERGEANT'S, ZODIAC and many more.
Depending on your location, some pet supply stores will carry Advantage and/or Frontline for kittens, but even if you buy this from your vet, make sure the box says 'for kittens' and is not for adult cats or dogs.
You did the absolute right thing in combing her and bathing her and the best thing to do with bathing, is to use original blue Dawn dishwashing soap. If you don't have that, any dishwashing soap in the house, will do. However, since you bathed her twice already, I would not repeat that, but wait for her to see the vet, tomorrow.
If you feel you may not have rinsed her properly, you can wipe her down with a warm, wet cloth, to remove any residue from her skin/coat.
Even though she doesn't seem to have a bad infestation (thank goodness!), it's possible, once fleas were brought into the house, your home could become infested, so play it by ear, but if you notice any live fleas around your home or on her, after the topical flea treatment is applied, you might have to treat your home, as well.
You can hire an exterminator who specializes in fleas, like Fleabusters, or buy their supplies to treat your home. I would not use their products ON your kitten, just to treat your home.
They have many offices nationwide, so hopefully, there's one near you, if you should need their services. I, personally have used them and they were great!
Another thing you might consider to treat your home is food grade diatomaceous earth (DE). You can sprinkle in in your carpet, along baseboards, under furniture cushions, etc. and it is not harmful for humans or pets.
I hope all will be well with your furry little girl and you will see no more fleas!
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