Nah, you're good.
He absolutely did, but all throughout the OT the only people that are told to be like sheep, is Israel. Whether it's the prophets, or David referring to himself as a sheep. Sheep always mentioned Israel. A fold, doesn't denote a different species, only a different location. They were all His sheep, but in different locations. At that time, He was talking to Jews.
This can be proven by going from the verse you linked, about having "sheep which are not of this fold".
That verse you linked is John 10:16. If you read the rest of the verse:
John 10:16 And other sheep I have, which are not of this fold: them also I must bring, and they shall hear my voice and there shall be one fold, and one shepherd.
In that Romans quote Paul made at the end. He's quoting from the book of Isaiah. Isaiah 11.
If you read the rest of that chapter, you can see that it's not only talking about what Jesus did for us, but also that this is talking about the regathering of the 12 tribes that were scattered abroad, bringing them together again in the last days to again be Israel. Saying that Ephraim will not envy Judah, and Judah will not vex Ephraim. This part hasn't happened yet, because Ephraim still envies Judah, and Judah, as this entire post has shown, still vexes Ephraim.
A couple verses before that shows you who the nations are.
Revelations 21:21 - And the twelve gates were twelve pearls: every several gate was of one pearl: and the street of the city was pure gold, as it were transparent glass.
Earlier in Revelations 21, it talks about the 12 gates, and how each of them had the name of each tribe of Israel on them. Those are the nations that were saved. The nations that are saved, are the multitudes of people that are saved, from all over the world, that are sheep of other folds, but as Jesus said in John 10:16, those sheep will come together to be one fold, with one shepherd. That fold, is Israel. Of which, there are 12 tribes.
Isaiah 2:2 - And it shall come to pass in the last days, that a mountain of the Lord's house shall be established in the top of the mountains, and shall be exalted above the hills; and all nations shall flow unto it.
Isaiah 2:3 - And many people shall go and say, Come ye, and let us go up to the mountain of the Lord, to the house of the God of Jacob; and he will teach us of his ways, and we will walk in his paths: for out of Zion shall go forth the law, and the word of the Lord from Jerusalem.
This is talking about in the last days, people saying that we should learn the ways of God, and walk in His paths.
As I pointed out, the sheep of different folds, will come together to be the same fold - Israel.
Absolutely it is. But it gives light to how it was back in the Torah. It was always said, in many verses, in many ways, that if a stranger wishes to be Israel, all they have to do is to take up Israel's ways. But, they weren't to be Israel and the strangers. It was simply, Israel. They were to be as ones born in the land, meaning that either they got to choose which tribe to become, or they were forced into certain areas. Allow me to submit to you, that as it says in Ezekiel 47:23, that they weren't forced to be in any-one-tribe, and that they got to choose which tribe they'd reside in. Just as it'll be again in the end of times, when Israel is brought back together to worship once more.