is it Oh and it's "you're". or Oh and it's "you're."?

Stylistically, including the period inside the quotation marks is usually preferred. However both options are acceptable.

The period goes inside the quotation marks-for sure

You're putting quotations around a specific word; the period goes after the quotation mark.

In American formatting, comma and period placement when quotation marks are present does not follow logic; they always go inside, even if the phrase doesn't originally contain such a mark.

Example: I love Hemingway's "The Old Man and the Sea."

British formatting, however, does follow logic. If you're not quoting something that already has a period or comma, it goes outside.

Example: I love Hemingway's story "The Old Man and the Sea".

I include both so you understand why people will give you both answers. Format it according to your region.

Well, first of all, you wouldn't be able to end a sentence with "you're" anyway. You would have to use

"you are". But as far as the quotations and period go, if you are quoting someone, but your own sentence goes on before and after the quotation, then your period would go inside of the quotations. However, if your sentence ends at that point, it would be quotations then the period.

Example: I was talking to my mom and she said "I don't think that is possible." but I think she is wrong about that.

Or: When my dog saw me, she happily hopped up and down and cried "Woof, woof".

I think.

If the entire sentence is in quotation marks, then the period goes inside the quotation marks.

In your example "you're", it is only that word, hence, it is "you're".

Oh, and it is "you are".