Well, I am a professional number theorist, so let me give you some feedback that you don't seem to have received yet:
Your paper containing an elementary proof of Fermat's Last Theorem is wrong.
This is what I think, and I am confident that this is what more than 99 out of 100 professional number theorists would think. Here by "wrong" I mean as a real person would use the term: i.e., probably wrong. I obviously don't know that it is wrong, and I couldn't without reading it, but in real life there is almost nothing that one knows is right or wrong: we have to go based on probability. Let me try an analogy: suppose I am an amateur aerospace engineer. I claim that I can walk into anyone's home and, using only the materials that are already there, build a ship that can safely carry me to the moon and back. Wouldn't you say that I'm wrong? Wouldn't you say that, if anything, the fact that we have been to the moon and back gives us a better sense of the resources necessary for that, and that gives you more confidence that my estimation is wildly off? That while it's of course possible that I'm right, if I were I would have to be in possession of such vastly superior knowledge and expertise that I could easily provide evidence of it on a smaller scale? That's pretty much how we number theorists feel.
Let me make one point about amateur mathematicians: it is exceedingly rare for an amateur mathematician to solve a problem that has been worked on unsuccessfully by the mathematical mainstream, but it has happened sometimes (more or less depending upon what you mean by an amateur mathematician, but if for instance you count brilliant young people without a college degree: sure, it has happened several times). However I know of no examples in which an amateur mathematician has solved a significant mathematical problem without having done other substantial mathematical work already. So...is this your first math paper, or the first substantial piece of mathematics you think you've done? If so, I really think it's wrong: that's just not how success in any field works. Nobody picks up a tennis racket for the first time and discovers they can play at the professional level. On the other hand, if you do already have published papers, then certainly mention that in your correspondence: it will make a big difference.
Anyway, if you want to find out why your proof is wrong, then yes: I agree with the other answers who say that you should pay to enlist the services of a tutor. If you go to any math department with number theorists and say that you have reading and thinking about FLT and have some ideas you'd like to clarify and are willing to pay, say, $30 an hour to get one-on-one tutoring, I think you're very likely to find some takers.
Let me say finally that my goal in writing this answer is not at all to crush your dreams. Rather, I hope that you actually like mathematics enough to move past your thought that you have proven FLT and engage with the subject matter more deeply. Mathematics is a lot deeper and richer than I think you know...in some wonderful ways. Good luck.