The original version of this question left out some important context that
has since been supplied in comments on another answer,
and has an interesting mix of self-deprecation and boasting,
both of which might lead readers to have less confidence than perhaps we should
in the things you are saying.
You're young (I assume), so this may just reflect a lack of maturity
(due to your age) which you may correct as you gain experience.
This is to say you are still on somewhat shaky grounds with regard to getting
interest in your work from a bunch of strangers on the Internet, but not
the same kind of shaky grounds as someone who has been doing his work in
his own way in secret in a basement for 40 years before announcing it.
(You have much better prospects for making a useful contribution.)
I would say by all means try to write this up as well as you can with the
help of the people you know who can comment intelligently on what you have done.
You may want to go through several rounds of getting comments and suggestions
and rewriting your work accordingly.
You should also carefully read any papers you can find on this topic,
especially survey papers
(there are some references in https://mathoverflow.net/questions/979/,
trying to understand what others have tried to see if their methods are
someone like yours (even if they describe things in different words).
To get any kind of useful publication credit within four months
seems unrealistic to me. The time it takes to get through the
review process for a refereed journal is typically much longer than that,
and I can't think of any other type of publication that would give you
the kind of recognition that would be an advantage on a university application.
If you can get an introduction to an active researcher in mathematics
(or even computer science, which has an entire subfield for this kind of thing)
then pursue it; perhaps you can even get a letter of recommendation
based on your work.
Another possibility, if there is any chance to attach a document to your
university application, is to submit your "paper" with your application.
Of course you will want to make sure that what you submit is something
a math professor might be interested to read and not throw down in despair.
Then, rather than relying on the recognition that comes from publication,
let your work simply speak for itself.
There are two very likely reasons for your work to be unpublishable:
- There might be a subtle but fatal flaw in your reasoning.
- Someone may have done it before in a publication you either have not found yet or did not fully understand.
But even if one of these things turns out to be true,
I believe your work could still be useful to you in your university application.
If someone who has not yet started university training can even make
a halfway credible attempt to create some useful and novel mathematics,
I would hope it would be of great interest to a university.
Once you get into a university, you will (sooner or later) have the kind
of access to researchers in mathematics (professors at your university)
who may become interested in what you have done.
If the idea is a good one, you may find that your professors can help you
get it published. You will already be at the university, of course,
but a publication could help your application to a graduate program later.