See, I’d thought that River giving him all of her remaining regenerations was going to be the thing that got around the “Doctor only has 12 regenerations thing” too, but that wasn’t proven true.
Instead, I think that was sort of the workaround for River herself (who is a Time Lady) to not regenerate into another form in the future.
The Doctor has more regenerations now thanks to the Time Lords granting him a new set of regenerations in the Christmas special when Eleven changed into Twelfth.
They said in LKH that River didn’t give him her regenerations. Melody “used all [her] remaining regenerations in one go”. It’s why she collapsed and had to be hospitalized; that intense blast of energy at one go could have killed her.
So she didn’t transfer the regenerations; she used them, all of them, like a combination defibrillator, antidote, and cellular re-generator all in one. She brought the Doctor back to life from the dead, it takes more than 1 to do that. Imagine asking a doctor or EMT what takes more effort and resources: stabilizing a poison patient or bringing someone back from death with no damage physically or mentally when their brain hasn’t functioned in over a minute. That’s what Melody did.
You can see her regeneration energy entering his body through her hands and kiss…
… and then leaving his body through his hands. See how the energy trail starts from his hand and goes into the air?
That’s what all that time energy in the air is: the other 10 Melody Ponds having been used up and expelled.
Vilenye wrote a lovely fic about that scene and the Doctor seeing each of those other Melody Ponds that give up themselves for his life. It’s called The NeverWeres of River Song. I heartily recommend it!
Does that help?
(images are not mine)