"If he had won the nomination, I would have registered to vote, unbelievably, for a Republican candidate."
If you had registered to vote you could have voted in the presidential primary for Ben Carson. Also, you could have voted in local elections that often have the most impact on your life.
"But here’s the thing: no matter who is in office, as far as my thirty years of life experience can tell, not much changes."
This is a typical justification for voter apathy - and rightly so. People need to feel that their vote matters before they'll expend the effort to learn about the issues and the candidates' position on them. Many states have a "straight party" vote option relieving voters of need to be informed.
"The political party system fosters an “us against them” mentality in a country that desperately needs unity. "
I think the blame is better placed on our single seat, single choice plurality voting system than on the political party system. If we had multiple seat larger districts with political party proportional representation people would feel that their votes are more important.