He didn't say He only died for His sheep. I could say I went to the store for John. That doesn't mean I didn't also go to the store for Joe. That's why taking Scripture out of context leads to error. If that's your argument then only those Jews would be saved. In context Jesus said He had only come to the lost sheep of the house of Israel. So, in context, the sheep He was speaking of, were Israelites. If they're the only ones He died for, as you say, then no Gentiles can be saved. So, you see, when we look at the Scriptures, IN CONTEXT, your argument falls apart.
23 But he answered her not a word. And his disciples came and besought him, saying, Send her away; for she crieth after us.
24 But he answered and said, I am not sent but unto the lost sheep of the house of Israel. (Matt. 15:23-24 KJV)
However, John tells us that Jesus came so that all men could be saved.
There was a man sent from God, whose name was John. The same came for a witness, to bear witness of the Light, that all men through him might believe. He was not that Light, but was sent to bear witness of that Light. That was the true Light, which lighteth every man that cometh into the world. (John 1:6-9 KJV)
Here John tells us that Christ enlightens every person coming into the world that they might be saved. He uses the singular, man, indicating every single man or person. There's no way around this. It proves grammatically that all can be saved. In this passage "all" grammatically is every single person.