Hola Pati,

this sentence:

Me hice construir un anexo al lado...

using the reflexive pronoun sounds as if the subject did the action himself/herself, but this is a structure that follows the same pattern as that one explained in this lesson (there is a link at the bottom of the lesson that takes you here):

How to say to have something done

With that structure the reflexive pronouns are used but the action is performed by someone else. If we forget for a moment about the verb "hacer" and just use "construir", the sentence could have also been (with the same effect):

Me construí un anexo al lado... 

This again sounds as if you did it yourself but that is not normally the case; it indicates someone else (the builders) did it. 

I hope this clarified it.

Saludos

Inma