Think about it: Marty goes back to 1955 in Part 1 and helps his parents fall in love again. Well, when Marty went back to 1985 he created an alternate timeline where his parents are rich. There are alternate George, Lorraine, Dave McFly, and Linda McFly, but strangely no Marty. So where is this alternate timeline Marty and why is he not present?
When Marty initially returns to 1985 near the end of the first film, he chooses to arrive ten minutes earlier than the point in time when his younger self left 1985 to begin with. He then runs over to Lone Pine Mall, hoping to reach Doc before he's shot by the Libyans, but he's too late, and sees Doc being shot again, and a younger version of himself inadvertently using the time machine to travel back to 1955.
Since Marty is now shown to be at Lone Pine Mall though, rather than Twin Pines Mall, as it was called earlier in the film, we know he's already in a different timeline than the one he originally departed from, despite the similarity of the events taking place. So the Doc he sees being shot by the Libyans for a second time isn't quite the same Doc he knew originally. Rather, this is a version of Doc who lived through an alternate version of history, as a result of the changes Marty made in 1955. The same applies to the version of Marty he sees travelling back to 1955. This is the alternate version of Marty who was raised by the alternate versions of George and Lorraine mentioned in your question.
So when Marty returns to the McFly household, of course there isn't an alternate Marty there, because we just saw him go back to 1955. It does beg the question of what happened to the alternate version of Marty after he arrived in 1955, but there's already another question addressing that point.
I think you're maybe thinking that when Marty goes back in time, a new universe is created with all his changes in it.
This is not the case - there is only one timeline, which gets changed with trips back in time. Dave and Linda at the end of the movie are not new people from a new universe, they are the same Dave and Linda that we saw at the start of the movie, but they have been altered. It's like rewinding the tape and recording over it.
So as to your question about "Where is the Marty of the new Universe?" - you're looking at him! He's the guy acting so confused that Dave works in an office and Linda has lots of boyfriends.
Now it's a bit confusing because presumably there should be a Marty who knows all about George being a well-known author and Elaine being thin. But it's consistent through the movies that if when you travel through time and make changes, you keep your memories from the before the changes.