The Greek word /monogenes/ is the key here. I did a word study on this a number of years back. The word actually appears in the Septuagint (the Greek translation of the Hebrews Scriptures). Here it is actually used in reference to Isaac as the /monogenes/ son of Abraham.
Interestingly enough, Isaac was not the only son of Abraham and not even the first. Ishmael was born first and Abraham had six other children with Keturah after the death of Sarah.
So, /monogenes/ does not indicate that Isaac was the only son. The word comes from the combination of two other words -- /mono/ and /genes/. /mono/ is, of course, indicative of "one". /genes/ refers to kind. In a sense, then, /monogenes/ refers to "one of a kind" or "something wholly unlike any other".
Since Isaac was not the only son of Abraham, in what sense was he a one of a kind? Specifically, he was unique in his miraculous birth and in his being the fulfillment of the promise of God. No other son was born in fulfillment of a promise from God and no other son was born miraculously.
Jesus is identified as the /monogenes/ Son of God. Typically, this is translated as "Only Begotten". It is true that Jesus is not the only son of God or only child of God, because, as you identified, all of those who have faith in Jesus are children of God.
However, the Sonship of Jesus is unique. Indeed, His Sonship is wholly unlike any other. Its uniqueness is that it is eternal. Jesus never became a son of God, but was always the Son of God and God the Son.
So, Jesus is not the only son of God, but He is a Son unlike any other in His divinity.