Hey I have had high arching brows, high cheekbones and really high hard palate. Genetic?

It is not a syndrome. There is no specific relationship between high brows, high arched palate and prominent cheek bones. It is "genetic" in that you were born this way, but is is not "syndromic", meaning, there is probably nothing wrong or abnormal.
Very likely genetic. Our physical makeup is largely genetic but can be varied by environmental factors. Individuals with a really high hard palate are more susceptible to developing obstructive sleep apnea.