Well, you're asking about an area of law that is currently in a state of flux -- the sorts of innovations that are eligible for patent protection no matter how non-obvious they are. Until very recently, a machine-implemented method of performing little or no more than a mathematical algorithm was ineligible. Now, it's arguably eligible. If and when that issue reaches the Supreme Court, I'd expect it to be returned to where it was a few weeks ago.
I also come from a computer science background and have been working primarily in this area for the entirety of my patent career. So, I'm fairly familiar with the ways to express what you're doing in claim language that gets over than initial threshold.
You mention your method is unique -- I take that to be synonymous (more or less) with the patent requirement of "novel."
While you didn't mention it, the patent law requires more than simple uniqueness -- uniqueness in a manner that's non-obvious over what others have done/described.
Now, on to the questions you posed.
You're not sure it's unique. And, you'll never be sure. That's one of the risks you will have to accept (in some degree) if you enter the world of patents. The universe of things that can destroy your uniqueness is just too large to fully assess in any practical manner. If you've done a general literature search, it's probably not bad to conduct a patent literature search as well. Because many ideas go nowhere, the patent library is full of things not found in other literature. In addition, it seems the crazy days of the late 1990s filled the Patent Office with applications describing just about every idea floating around at the time.
You're not sure your idea is better than the others. That's not a requirement for a patent -- only novelty and non-obviousness. If you hope to attract investment capital, being better helps -- is probably absolutely necessary. But it's not necessary to obtain a patent (although it helps, in my opinion).
Regards.