You had a 3 month old Chihuahua and a 5 year old together? Seriously?
The only thing you can possibly do at this stage is let the vet look after her. She is in the best place and that's the only real comfort I can offer you. Poor little thing....I really hope and pray she will be OK. If she is generally strong and healthy she may pull through this with good care, and recover well. I do hope so. Trust the medical care she is receiving.
Unfortunately little children do not know their own strength and clumsiness, especially with a very tiny puppy. When she recovers and comes home you are going to have to speak very seriously with your 5 year old boy/(girl?) and take a LOT of care with her. Crating her in a large crate for a while, as she recovers properly might be sensible even though it sounds awful. But don't leave her there all the time of course. Only to prevent accidents with your child and her. She is very tiny and very fragile.
I hope for a good outcome and send the little pup my heartfelt kindest wishes for her recovery. Bless her Soul.
I know that this is not what you want to hear right now, but this is why it is such a bad idea to combine small children and toy dogs. Kids don't know that what they do can have such a devastating, lasting effect on something and they are also not yet coordinated enough to conduct themselves around something as frail as a toy breed puppy.
The problem with Chihuahuas is that they are one of the only breeds that has a molera, which is an opening in the skull similar to the fontanel in a human baby. The thing is, in a human baby the fontanel closes. In a Chihuahua, the molera is open for the life of the dog. This can be good and bad. If your puppy has brain swelling, the molera will allow for the expansion of the swelling brain, whereas a closed skull would not. However the molera also probably had something to do with the fact that the brain was injured in the first place. In a puppy with a closed skull the brain may not have sustained the injury at all, but depending on how severely your child injured the puppy, it may have become injured anyway.
The vet's is the best place for your puppy to be. When your puppy comes home, however, you may want to consider rehoming him because it has already been proven that there is the possibility of a serious injury to the puppy in your home. If the puppy sustains a second injury similar to this one, or even sustains a good rap to the head for ANY reason, it may be fatal the next time because of this original injury.
Please let us know how the little one makes out. I will be thinking about him.