It certainly means that peace has not come yet, but there is nothing in either passage that says that when the Messiah comes peace will automatically start.
There is no timeline for this, and with a risen Messiah who is immortal, the last days, the Messianic times, can go on until the job is done, even for 2000 years or longer.
This is what motivated reasoning looks like. Your motivation is to try to reconcile OT messianic prophecy with your faith-based belief that Jesus fulfilled it. Absent that, you'd see what the skeptic sees. You'd see a list of qualities of the Messiah from the OT and those of Jesus from the NT, and you'd see that they contradict one another in a variety of places, one being that the era of world peace didn't arrive during Jesus' life, and that therefore this was not the one predicted. But you simply will not allow your mind to be led to that conclusion, so you look for ways to overlook the contradiction as you're doing here.
What you're ignoring is that the description of the Messiah is how one identifies him. You're willing to say that Jesus didn't need to satisfy these requirements in his lifetime, which is not what a skeptic would say. And if one is free to that, then he can call himself the Messiah and that he fulfill those requirements someday. The skeptic says, "On that day if it comes, I'll know that you are the Messiah, but today, you're just another guy who doesn't match the description and I have no reason at this time to believe that you ever will."
That's how an open-minded person evaluates evidence. He lets it take him to sound conclusions about it, which in this case is that Jesus didn't fulfill messianic prophecy. But a person who has decided by faith that Jesus was the person described is a motivated thinker, and will come up with anything that he can to try to make that round peg fit into that square hole, including just simply ignoring the discrepancies or allowing for them to manifest in the future.
Imagine a fortune teller telling you that you would be killed one day by an old, bald man and you believed that. Later, a young man with a full head of hair is glaring at you menacingly, and you shoot him dead thinking that this must be the one the fortune teller warned you about. Never mind that a list of the prophecies one (old, bald) doesn't match the description of the person you are convinced is that person. When the glaring contradiction is pointed out to you, you say that the oldness and baldness haven't manifest yet, but the guy you killed was definitely the person the fortune teller foresaw.
THAT'S motivated thinking, and its only use is to defend wrong beliefs from evidence. That's also the description of a confirmation bias. And that's what you're doing.