This was one of my interests a few years ago. I was born with mild Goldenhar syndrome - I have a asymmetrical face, some bone missing from my jaw, I had a wide mouth due to an extremely rare cleft lip (a type 7) that needed surgery (before it was corrected I could not suckle and had to lick milk like a cat) and I a few cysts on my left ear removed. I also have a mild heart abnormality.
DiGeorge syndrome is one of several 22q11 deletion syndromes. They are also known as Catch 22 syndromes - there are many different types. Yes, children with 22q11 deletion syndromes often have AS and autism in childhood - however, when most reach adulthood they fair much worse and are more often diagnosed with schizophrenia. Thus, the 22q11 deletion condition is researched for candidate genes for schizophrenia. Also, the condition is associated with cleft palate and distinctive broad nasal bridge etc.
That said, there maybe a spectrum between 22q11 deletions (velocardiofacial syndromes) and other "milder" craniofacial abnormalities that include Goldenhar and hemifacial microsomia, so called facio-auriculo-vertebral syndromes.
Also, 1/3 of children with Goldenhar have mild autistic like traits, including AS. I would suggest that small deletions in the 22q11 region might cause cases of hemifacial macrosomia and Goldenhar, and also explain why people with these conditions have a much greater risk of developing ASDs.
If you want to be checked for 22q11 or other deletions - ask for a FISH analysis. It might be free depending on where your living e.g. UK (I think its €200 here in Ireland).