Though it did seem like a Sontaran from the blur, as stated by alexwlchan, I agree more with Immotbanksy’s answer. It didn’t look like a Sontaran under the blanket and Sontarans are obsessed with war, so this seems out of place for them. Altering the course of history in such a meticulous and subtle way, even going so far as being with you at all times, always in hiding (being that the premise of such a creature, stated right at the start of the episode) just doesn’t fit.
In addition, I also find that their hands make a compelling case:
Look at that. I find it very hard to believe that from everyone sharing this same nightmare (and every one should experience it some time in their lives, according to the Doctor’s theory) there are not a significant number of reports of people also stating “and the hand felt weird, like if it were the wrong shape”. Even if many people were in enough of a shock to not notice, I find it doubtful that from everyone having this dream, a high number wouldn’t have noticed.
That said, I do also find it a bit weird it would be another child, simply from the way it behaved. I mean, the Doctor, Rupert, and Clara were shouting about acting really scared. I find it hard another child would have acted in such a manner, even approaching them and removing the blanket. It wouldn’t be impossible, I just think it would be very odd behaviour.
The point does seem to be that it doesn’t matter, but it would still be nice to have an answer, particularly to “why does everyone have this dream, then?”. Is it just something in our brain, in the way we evolved, and we all share some genetic trait that causes it?