Don't let yourself get discouraged. It is wonderful that you have such aspirations!
But, in my opinion, it would be best to aim for developing your skills, poise, maturity (in the sense of mathematical sophistication), and confidence, by undertaking a series of "smaller" and somewhat challenging steps:
- researching; engaging in an exchange of ideas;
- consulting peers;
- consulting faculty member(s);
- continue researching;
- presenting your research in a poster session at a conferences for undergrad/grad research;
- revising your paper;
- presenting your paper - at an informal gathering -- then perhaps, to your department;
- revising your paper;
- submitting a paper to journals that publish primarily undergraduate and graduate research/articles, etc.;
- revising as suggested by editor (if it hasn't been rejected...etc.);
- resubmitting paper;
- Did I say revising?
Better to experience, learn, and build from a series of small successes (even perhaps a few not-so-successful experiences) en route to publication, than to try, from the starting line, to take a huge leap for which you may not be prepared and will likely fail.
Note: There are also magazines and journals whose target audience is undergraduate and graduate students, and hence much more likely to showcase the work of students. (I'm assuming you're a student, given your reference to your "teachers.")
See for example the MAA's (Mathematical Association of America) site addressing venues for publication of undergraduate research in mathematics: MAA webpage here
Excerpt from the site:
Venues for Publications
In addition to the traditional mathematical journals where the authors are usually research faculty, there are some journals that specialize in mathematical research done by undergraduates. These include the Pi Mu Epsilon Journal, The Pentagon: The Official Journal of Kappa Mu Epsilon, Rose-Hulman Undergraduate Mathematics Journal, Furman University Electronic Journal of Undergraduate Mathematics, and the Morehead Electronic Journal of Applicable Mathematics.
These journals are all excellent venues for undergraduates to present their research, however it is generally accepted that they are not at the same level as traditional faculty-oriented journals.
[Of all such journals, however, I'd suggest looking at some issues of] the new undergraduate research journal, Involve – A Journal of Mathematics, which is in a class by itself. The journal boasts an impressive editorial board of distinguished faculty and articles are to be reviewed by MathSciNet and Zentralblaat Math, a known distinction for quality journals This distinction also allows student work to be more easily searchable and citable! [Brackets mine.]
(from MAA Resources)
More information on Involve: A Journal of Mathematics can be found here.
I'd encourage you to look into some of these sites and publications!