NA (New Adult) is generally a book that has a Young Adult protagonist, but would deal with more adult themes.
YA (Young Adult) usually has a protagonist who is older than the target audience. Typically, the main character is a teenager. However, if you're writing a series and said character ages with each book, you can get up to early twenties with a character.
The setting doesn't really influence Young Adult. That's a bit of a myth. You could have someone who is out supporting themselves, and working, but they might just be seventeen. I don't think you should worry too much about the fact they're a college student.
To be perfectly frank, most people these days don't consider themselves an adult until they're about 21/22 years old. That being the case, I think you should focus less on the age of your character, and more on the narrative. Let's not forget that there are some books with young characters that are certainly not young adult. Elizabeth Bennett was only twenty in Pride and Prejudice, but that's not classified as Young Adult merely because she was barely out of her teens. Likewise, Lolita has an exceptionally young female leading character (admittedly she's not the one leading the narrative but she is the focus of the novel), and there's not way that's Young Adult.
So, I guess my advice here would be that you should let your book be what it needs to be. You are doing seriously well so far, don't get bogged down with little niggling issues like the age. Decide your audience when you're done, and enjoy the story writing process.
I mean, you're thirteen, and if you like it then that would make it totally suitable for your age group.
Besides, (as much as I hate pulling this as an example) Edward Cullen was over a hundred years old, and he was a YA main character.