"CHrist" is a greek term, which is translated from the Hebrew, a term meaning 'annointed one'. THere were two annointed ones in Hebrew Culture. One was the High Priest, the other was the King.
Isaiah 9:7 was indeed talking about someone in the house of King David.
It was talking about Heizekal, the son of King Ahaz. Heizekal is literaly translated as 'God is our Might'.. or "mighty god". That was one of his royal names.
Isaiah 7:14 does not say virgin. Almah is hebrew for 'Young maiden', and refers to age. If you read Isaiah 7-14 to 8:18 in context, you will see that Isaiah was talking about the birth of his own son.
8:3-4 shows that he 'went ot the prophetess and insured she conceived',
8:18 says the signs that Isaiah revealed where himself and his sons.
the prophecy was 'Before that child knows good and evil' (a certain time frame, from conception to the time the child is about a toddler),
the king of assyeria will lose. This is in regards to a war King Ahaz
was waging with the Assyeria at the time.
This was an after the fact writing of the claim of Isaiah to have given a sign to King Ahaz. If you read it in context, it has nothing to do with a messiah being born 700 years later.