This article focuses on Rabbi Ishma'el's 13 rules and explains both how they work as well as what current rules are. I'm extracting some items:
The Rabbis checked and limited the force of the Kal Ve- Chomer by
applying the principle of Dayyo, i.e., that it is quite suffcient that
the law in respect of the thing inferred should be equivalent to that
from which it is derived. The origin for this principle is BiblicaL.
The principle of Gezerah Shavah is subject to a number of limitations.
Thus we are told, that even though a man may project a Kal Ve-Chomer
on his own, no man may advance a Gezerah Shavah unless he has received
it as a tradition from his teacher and his teacher from his teacher,
all the way back in time to the Lawgiver, Moses.
Most of the other rules apply to specific situations where Torah verses contradict each other or they relate to the order of specifics and generalizations. I couldn't locate anything in the article that states if one can devise his own analogies. However, in viewing the examples and seeing how complex it is to apply these rules in most situations, I'm humbled by how difficult it is to analyze it and arrive at one's own conclusions.