Question Involving Sex VS. Gender

October Momma • 22 year old happily married mother of boy girl twins, Emma and Alden, born 10/11/17😊
So I have a question that I've been curious about for sometime. The reason I have decided to ask on here is because I have seen many lively debates on the sex vs. gender topic and the most common thing I see is that their sex is determined by the sexual organs they are born with but their gender is determined by what they feel they are meant to be. This left me curious about a few things that I was hoping those from either side of the debate could clarify. I personally will not add my own personal opinion on the matter because opinion is not fact therefore my opinion is pointless. 
So say you meet a person whose sex is male but they say their gender is female. Because of this they have had surgery to change their sex organs to resemble to gender they say are. Now if they were asked for their sex, not their gender, would it not still be male since sex is what you are born with and gender is what you feel you are? If you never have any surgery, but feel you are he opposite gender what sex do you mark that you are? There are government forms and job applications that ask for sex, not gender. If the terms are not interchangeable, wouldn't you have to mark the sex that you are, not the gender you are? In a nut shell, if sex is what you are born with and gender is what you determine yourself, if you determine your gender is the opposite of what you are born with then isn't it also true that your sex never changes and if asked your sex not your gender you would have to give your sex and not your gender as a reply? I'm not talking about someone coming up to you and asking, I'm talking about job applications, DMV forms, marriage licenses, and other government forms that do not ask gender.